# Principle Component Analysis

library(readr)
library(ggplot2)
library(lattice)
library(ggridges)
library(ggvis)
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library(ggthemes)
library(cowplot)
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## Attaching package: 'cowplot'
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library(gapminder)
library(gganimate)
## No renderer backend detected. gganimate will default to writing frames to separate files
## Consider installing:
## - the `gifski` package for gif output
## - the `av` package for video output
## and restarting the R session
## 
## Attaching package: 'gganimate'
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##     view_static
library(dplyr)
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## Attaching package: 'dplyr'
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##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(tidyverse)
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## ✔ tidyr   1.3.0     ✔ forcats 1.0.0
## ✔ purrr   1.0.1     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter()     masks stats::filter()
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library(grid)
library(gridExtra)
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## Attaching package: 'gridExtra'
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##     combine
library(RColorBrewer)
library(readr)
#Covid-liver cancer Example
Cancer<- read_csv("~/Downloads/Cancer_Breast.csv")
## Rows: 379 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Survivor
## dbl (7): Age, Stage, Tumor Size, Regional Node Examined, Reginol Node Positi...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Cancer
## # A tibble: 379 × 8
##    Survivor   Age Stage `Tumor Size` Regional Node Exami…¹ Regin…² Survi…³   Sex
##    <chr>    <dbl> <dbl>        <dbl>                 <dbl>   <dbl>   <dbl> <dbl>
##  1 Alive       68     1            4                    24       1      60     0
##  2 Alive       50     2           35                    14       5      62     0
##  3 Alive       58     3           63                    14       7      75     0
##  4 Alive       58     1           18                     2       1      84     0
##  5 Alive       47     2           41                     3       1      50     0
##  6 Alive       51     1           20                    18       2      89     0
##  7 Alive       51     1            8                    11       1      54     0
##  8 Dead        40     2           30                     9       1      14     0
##  9 Alive       40     4          103                    20      18      70     0
## 10 Alive       69     4           32                    21      12      92     0
## # … with 369 more rows, and abbreviated variable names
## #   ¹​`Regional Node Examined`, ²​`Reginol Node Positive`, ³​`Survival Months`
str(Cancer)
## spc_tbl_ [379 × 8] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ Survivor              : chr [1:379] "Alive" "Alive" "Alive" "Alive" ...
##  $ Age                   : num [1:379] 68 50 58 58 47 51 51 40 40 69 ...
##  $ Stage                 : num [1:379] 1 2 3 1 2 1 1 2 4 4 ...
##  $ Tumor Size            : num [1:379] 4 35 63 18 41 20 8 30 103 32 ...
##  $ Regional Node Examined: num [1:379] 24 14 14 2 3 18 11 9 20 21 ...
##  $ Reginol Node Positive : num [1:379] 1 5 7 1 1 2 1 1 18 12 ...
##  $ Survival Months       : num [1:379] 60 62 75 84 50 89 54 14 70 92 ...
##  $ Sex                   : num [1:379] 0 0 0 0 0 0 0 0 0 0 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   Survivor = col_character(),
##   ..   Age = col_double(),
##   ..   Stage = col_double(),
##   ..   `Tumor Size` = col_double(),
##   ..   `Regional Node Examined` = col_double(),
##   ..   `Reginol Node Positive` = col_double(),
##   ..   `Survival Months` = col_double(),
##   ..   Sex = col_double()
##   .. )
##  - attr(*, "problems")=<externalptr>
#Get the Correlations between the measurements
Cancer$Stage<-as.numeric(factor(Cancer$Stage, labels=c("1","2","3","4")))
Cancer1=cor(Cancer[-1])
colMeans(Cancer1)
##                    Age                  Stage             Tumor Size 
##             0.07928344             0.27473584             0.27737917 
## Regional Node Examined  Reginol Node Positive        Survival Months 
##             0.20965656             0.26124102             0.10305467 
##                    Sex 
##             0.13925661
library (ggplot2)
ggplot(Cancer, aes(x=Stage, fill=Survivor))+geom_boxplot()+ labs(title='Survivorship comparison')

ggplot(Cancer, aes(x=Survivor,y=Stage)) + geom_boxplot()

## From the plot we can see that the survival rate for stage 1-2 is more, while in stage 2-3 there are no survivors. 


# Using prcomp to compute the principal components (eigenvalues and eigenvectors). With scale=TRUE, variable means are set to zero, and variances set to one
Cancer_pca <- prcomp(Cancer[,-1],scale=TRUE)
Cancer_pca
## Standard deviations (1, .., p=7):
## [1] 1.4982562 1.0851943 1.0302880 0.9698062 0.9386874 0.7121769 0.4327057
## 
## Rotation (n x k) = (7 x 7):
##                                PC1        PC2          PC3         PC4
## Age                    -0.21487519  0.2043145  0.027261393  0.85973142
## Stage                   0.56017028 -0.3373169  0.011318788  0.11956737
## Tumor Size              0.57902017 -0.2934857 -0.007289973  0.15966422
## Regional Node Examined  0.23910247  0.6987477  0.329462796 -0.11137816
## Reginol Node Positive   0.45785153  0.3946611  0.191113542  0.03278061
## Survival Months        -0.18008353 -0.1898301  0.618720758 -0.33346116
## Sex                    -0.07446786 -0.2798176  0.686432853  0.31047844
##                                PC5         PC6         PC7
## Age                    -0.41336263 -0.03629602 -0.00410619
## Stage                  -0.21766761  0.18269976 -0.69082826
## Tumor Size             -0.13361696  0.13694401  0.71864375
## Regional Node Examined -0.03947383  0.57624593  0.00365182
## Reginol Node Positive   0.10540722 -0.76394463 -0.04789123
## Survival Months        -0.63971799 -0.15748760  0.05900235
## Sex                     0.58479969  0.07795267 -0.02241484
summary(Cancer_pca)
## Importance of components:
##                           PC1    PC2    PC3    PC4    PC5     PC6     PC7
## Standard deviation     1.4983 1.0852 1.0303 0.9698 0.9387 0.71218 0.43271
## Proportion of Variance 0.3207 0.1682 0.1516 0.1344 0.1259 0.07246 0.02675
## Cumulative Proportion  0.3207 0.4889 0.6406 0.7749 0.9008 0.97325 1.00000
## In Standard deviation we can infer that:
## PC1 is mostly driven by Tumor Size, Stage, and Reginol Node Positive, which all have relatively high loadings on this component.
## PC2 is mostly driven by Regional Node Examined, Reginol Node Positive, and Age, which all have relatively high loadings on this component.
## PC3 is mostly driven by Sex, Survival Months, and Tumor Size, which all have relatively high loadings on this component.
## There are negative loadings for some variables on certain PCs, indicating that they are negatively associated with those components. For example, Age has a negative loading on PC1, meaning that as PC1 increases, Age tends to decrease.


# sample scores stored in cancer_pca$x
# singular values (square roots of sevenvalues) stored in Cancer_pca$sdev
# loadings (eigenvectors) are stored in Cancer_pca$rotation
# variable means stored in Cancer_pca$center
# variable standard deviations stored in Cancer_pca$scale
# A table containing eigenvalues and %'s accounted, follows
# Eigenvalues are sdev^2
(eigen_Cancer <- Cancer_pca$sdev^2)
## [1] 2.2447716 1.1776466 1.0614934 0.9405242 0.8811341 0.5071959 0.1872342
names(eigen_Cancer) <- paste("PC",1:5,sep="")
eigen_Cancer
##       PC1       PC2       PC3       PC4       PC5      <NA>      <NA> 
## 2.2447716 1.1776466 1.0614934 0.9405242 0.8811341 0.5071959 0.1872342
sumlambdas <- sum(eigen_Cancer)
sumlambdas
## [1] 7
propvar <- eigen_Cancer/sumlambdas
propvar
##        PC1        PC2        PC3        PC4        PC5       <NA>       <NA> 
## 0.32068166 0.16823523 0.15164191 0.13436059 0.12587630 0.07245656 0.02674774
cumvar_Cancer <- cumsum(propvar)
cumvar_Cancer
##       PC1       PC2       PC3       PC4       PC5      <NA>      <NA> 
## 0.3206817 0.4889169 0.6405588 0.7749194 0.9007957 0.9732523 1.0000000
matlambdas <- rbind(eigen_Cancer,propvar,cumvar_Cancer)
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
round(matlambdas,4)
##                        PC1    PC2    PC3    PC4    PC5   <NA>   <NA>
## Eigenvalues         2.2448 1.1776 1.0615 0.9405 0.8811 0.5072 0.1872
## Prop. variance      0.3207 0.1682 0.1516 0.1344 0.1259 0.0725 0.0267
## Cum. prop. variance 0.3207 0.4889 0.6406 0.7749 0.9008 0.9733 1.0000
summary(Cancer_pca)
## Importance of components:
##                           PC1    PC2    PC3    PC4    PC5     PC6     PC7
## Standard deviation     1.4983 1.0852 1.0303 0.9698 0.9387 0.71218 0.43271
## Proportion of Variance 0.3207 0.1682 0.1516 0.1344 0.1259 0.07246 0.02675
## Cumulative Proportion  0.3207 0.4889 0.6406 0.7749 0.9008 0.97325 1.00000
Cancer_pca$rotation
##                                PC1        PC2          PC3         PC4
## Age                    -0.21487519  0.2043145  0.027261393  0.85973142
## Stage                   0.56017028 -0.3373169  0.011318788  0.11956737
## Tumor Size              0.57902017 -0.2934857 -0.007289973  0.15966422
## Regional Node Examined  0.23910247  0.6987477  0.329462796 -0.11137816
## Reginol Node Positive   0.45785153  0.3946611  0.191113542  0.03278061
## Survival Months        -0.18008353 -0.1898301  0.618720758 -0.33346116
## Sex                    -0.07446786 -0.2798176  0.686432853  0.31047844
##                                PC5         PC6         PC7
## Age                    -0.41336263 -0.03629602 -0.00410619
## Stage                  -0.21766761  0.18269976 -0.69082826
## Tumor Size             -0.13361696  0.13694401  0.71864375
## Regional Node Examined -0.03947383  0.57624593  0.00365182
## Reginol Node Positive   0.10540722 -0.76394463 -0.04789123
## Survival Months        -0.63971799 -0.15748760  0.05900235
## Sex                     0.58479969  0.07795267 -0.02241484
print(Cancer_pca)
## Standard deviations (1, .., p=7):
## [1] 1.4982562 1.0851943 1.0302880 0.9698062 0.9386874 0.7121769 0.4327057
## 
## Rotation (n x k) = (7 x 7):
##                                PC1        PC2          PC3         PC4
## Age                    -0.21487519  0.2043145  0.027261393  0.85973142
## Stage                   0.56017028 -0.3373169  0.011318788  0.11956737
## Tumor Size              0.57902017 -0.2934857 -0.007289973  0.15966422
## Regional Node Examined  0.23910247  0.6987477  0.329462796 -0.11137816
## Reginol Node Positive   0.45785153  0.3946611  0.191113542  0.03278061
## Survival Months        -0.18008353 -0.1898301  0.618720758 -0.33346116
## Sex                    -0.07446786 -0.2798176  0.686432853  0.31047844
##                                PC5         PC6         PC7
## Age                    -0.41336263 -0.03629602 -0.00410619
## Stage                  -0.21766761  0.18269976 -0.69082826
## Tumor Size             -0.13361696  0.13694401  0.71864375
## Regional Node Examined -0.03947383  0.57624593  0.00365182
## Reginol Node Positive   0.10540722 -0.76394463 -0.04789123
## Survival Months        -0.63971799 -0.15748760  0.05900235
## Sex                     0.58479969  0.07795267 -0.02241484
## Sample scores stored in Cancer_pca$x
Cancer_pca$x
##                 PC1         PC2           PC3           PC4          PC5
##   [1,] -1.441559363  1.84595445 -0.3691842456  0.8313546497 -0.332307184
##   [2,]  0.466697152  0.06803649 -0.6236808487 -0.3679040103  0.110810520
##   [3,]  1.724644704 -0.46933933 -0.1593826887  0.5351088884 -1.007021612
##   [4,] -1.727412749 -0.67153366 -0.6471303735 -0.0657071859 -0.534587533
##   [5,]  0.084534880 -1.24252757 -1.5702796993 -0.3040439925  0.527096385
##   [6,] -0.987174108  0.58301426  0.1669091720 -0.9999683133 -0.430923510
##   [7,] -1.289312885  0.33343114 -1.1225709379 -0.4660831193  0.647838054
##   [8,]  0.457476281 -0.43703336 -2.3348237400 -0.5798103154  1.901144959
##   [9,]  5.013544810 -0.35127563  0.3138865965 -0.6789485742 -0.346406933
##  [10,]  1.966110970  0.57900951  0.8436785098  1.1971488330 -2.024615276
##  [11,] -1.709742154  0.39272616 -0.8797546127  1.0395229446 -0.421546565
##  [12,]  1.323214712 -1.40692828  0.0010448762 -0.8532983622 -0.998148360
##  [13,] -0.047344848  0.20982069 -0.8615166802  1.1288786920 -0.430771477
##  [14,] -0.023379894  1.83512622 -0.8543600804 -0.5919635549  1.267459198
##  [15,]  1.042993427  1.19479846 -0.1106365956  0.7578922926 -0.309831792
##  [16,] -0.954171084  1.25373181 -0.8631921253  0.4922727293  0.235344753
##  [17,] -0.510183493 -1.74284660 -0.1083044907 -0.2184460954 -1.466753080
##  [18,]  0.248390384  0.43156365 -0.4623851738 -1.2333483190  0.363615703
##  [19,] -0.386424810 -0.37494859  0.5477775527 -1.3442739171 -1.122742523
##  [20,] -0.212235416  0.44848661 -0.0814638947  0.1978257208 -0.848560671
##  [21,]  0.001291199 -0.22401731 -0.1753398416 -0.9042251252 -0.381745196
##  [22,]  0.547237523  0.35323566 -0.8945832960  0.4857434118  0.105717976
##  [23,] -0.581794885 -1.07033107 -0.7283097731 -0.0629010628 -0.572677371
##  [24,]  1.484574719 -1.12275223  0.4930197218 -0.8534326311 -1.510109489
##  [25,]  0.730385134  3.01009366  1.5328340955 -0.0845516282 -0.807050880
##  [26,]  1.384044724  2.86730858  0.7935319092  0.4879719811 -0.466990302
##  [27,]  2.503197607  1.86942247  1.6035708576 -1.0898911376 -0.702827024
##  [28,] -1.094732396  0.13919430 -0.2430526831 -1.3348711724  0.009704223
##  [29,] -0.040233637  0.24894946 -0.5823916977  0.1870202613 -0.228150297
##  [30,] -0.913495245 -0.27255918 -0.2249052502  0.7136559763 -1.283048492
##  [31,]  0.044817272 -1.24749459 -1.5147400984 -0.3403352312  0.475434709
##  [32,] -1.310023914 -0.18810081 -1.5041631045 -0.0748728835  0.691915088
##  [33,] -1.750326793 -0.31441971 -0.3126381565 -0.1365620557 -0.754412318
##  [34,] -0.860691537  1.17774354 -0.4731321013  0.2383866081 -0.049714847
##  [35,]  1.293140200  1.12837700 -1.0955034983 -0.3513923420  1.283108823
##  [36,] -1.575412171 -0.65517742  1.1178980897 -0.0145585733  1.416899251
##  [37,]  0.505620687  0.48204717  0.6768751198  0.9826148200  2.080438807
##  [38,] -1.445729993 -0.53420180  2.0397881463 -0.4191403509  0.606045480
##  [39,] -0.240634131 -1.38008841  1.2981310791  0.0234566336  0.948153836
##  [40,] -0.335231355 -0.71567154  2.2622815166 -0.2598837684  0.304358552
##  [41,]  2.392046521 -0.75381886  0.6808155988  1.7849935943  1.462378918
##  [42,] -1.496209472 -0.05147919  0.8362058172  1.4463882147  1.234755769
##  [43,] -1.238156754 -1.73396163  1.0838915624  1.1966166369  0.342914980
##  [44,] -0.122858339 -0.41520397  1.7259286489  0.2467343049  0.834734733
##  [45,] -1.614959830 -0.21262796  0.8270352673  0.5084458503  1.653782254
##  [46,]  0.653344872 -1.45282335  1.6923961454  1.7730389364 -0.346353752
##  [47,] -0.903132282  0.00288121  0.2891894480 -0.3828977838  2.883679498
##  [48,] -1.570956435 -0.13307164  0.7378711359  1.2691205943  1.372131721
##  [49,]  0.407142180 -0.18484286  1.8224576827  0.3406571927  0.900265041
##  [50,] -2.095133885 -0.24603762  1.3075254314  1.5865972660  0.515650798
##  [51,]  0.145196356 -0.72051716  1.2885099274 -1.1072761596  1.854988517
##  [52,]  0.438754344 -1.67207421  0.9831353778  2.3512915236 -0.039137939
##  [53,]  2.005777230 -2.95342227  1.2688959631  1.7356814675 -0.406467811
##  [54,]  1.526981600 -1.02119752  1.4223445513  1.8001650835  0.106389455
##  [55,] -1.762004433  0.13389155  1.3060891880  0.4365138287  1.220327765
##  [56,] -1.584099552 -0.27233552  1.1461680461  0.3643457178  1.304773967
##  [57,] -0.496130040  0.33490544  0.2711418287  0.1648088615 -1.311783436
##  [58,] -0.310631363  3.07311289  1.8743230894 -1.7983452746 -1.034356670
##  [59,] -1.133478035  0.41599332 -0.4379284603 -0.8528069490  0.092369673
##  [60,] -1.203472671  0.78226143 -0.1914939617 -0.4844823758 -0.219974275
##  [61,] -0.899762531  1.31926126  0.1811318594 -0.4938217806 -0.418037102
##  [62,] -1.006446958  0.35539993 -1.2221294160 -0.3469217710  0.736595283
##  [63,] -0.437812701 -1.58636590 -0.8897438306 -1.2595916576  0.044579623
##  [64,]  1.712300783 -0.45593265 -0.1013381728  0.5911078860 -1.251280484
##  [65,] -1.263885916  1.17224839 -0.6291534095  0.9206949813 -0.255173442
##  [66,] -1.604219653 -0.82712464  0.0494208809 -1.5797529143 -0.620332594
##  [67,]  4.488026052  1.14176192 -0.1231038156 -1.5112898673  1.345935978
##  [68,] -0.665172931  0.68451038  0.1453995807 -2.0258292592  0.217431325
##  [69,] -1.668377900 -0.33091730 -0.6606673180 -0.0526400595 -0.390248550
##  [70,] -1.130422629  0.23695569 -0.1769384999 -0.7612337767 -0.266397542
##  [71,]  3.316812797 -1.81535426  0.5502180418 -0.2694003925 -1.764262412
##  [72,]  2.172380940  2.85911092 -0.9844345887  1.6403461146  1.175874251
##  [73,]  0.572326326 -0.34757898 -1.0234096521 -2.0869344002  1.187096201
##  [74,] -1.827615023  0.62057292  0.3016558087  0.2426806849 -1.315635893
##  [75,]  0.720276568  1.70219107  0.6872975038  0.8005007414 -1.037240682
##  [76,]  0.849193077 -1.14260361  0.1217975270 -0.0272015985 -1.564340163
##  [77,] -0.640547040 -0.61272303  1.3854969929  1.5959470836  0.358667424
##  [78,] -0.095120639 -2.25942107  1.7743414136 -0.8570595769  0.490508151
##  [79,] -0.045215749 -1.67214619  1.1930256589  0.3311124134  0.788844783
##  [80,] -1.769164273 -0.22777378  0.5215512977  1.9330657865  1.230687259
##  [81,]  0.718379560  0.42702578  2.7049430509  0.0009902972  0.427134177
##  [82,] -1.678008963 -0.30727716  0.8345249461  1.7090923528  0.957971947
##  [83,] -0.895860760 -0.84819969  1.0351097886  1.6955225348  0.543187444
##  [84,] -1.627068924 -1.17405222  0.1883777552  0.6241466387  1.941501550
##  [85,] -1.331489281 -0.34160016  0.9121167916  0.1344506975  1.691751149
##  [86,]  0.909892498 -0.53731582  1.4060161653 -0.0311065615  1.547734256
##  [87,]  2.680823986 -2.87516871  1.2736995009  0.6959415006  0.332021211
##  [88,]  1.353531002 -2.37316783  1.3254482077  0.7127875562  0.214693076
##  [89,] -1.678967186 -0.70552936  1.6695940259  0.1038284595  0.653638646
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## [158,] -1.567211240 -0.76592187 -0.0382695651 -2.2426462201 -0.151819917
## [159,] -0.656681669 -1.17053344 -1.0085651375 -0.1509452878 -0.245449969
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## [178,] -1.150520519 -0.39541176 -0.6403158755 -1.4507416448  0.354044928
## [179,]  1.562083350  2.47954880  0.2323943105 -0.3200123444  0.378480572
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## [183,] -1.442466409  0.10416344 -2.2744315999  1.2646597948  1.004394643
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## [190,] -1.117892469  0.18858115 -0.3253204166 -1.3032488160  0.106289330
## [191,] -0.433517740 -0.06760578 -0.8846842302  0.3292279071 -0.195203996
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## [194,] -0.671437346 -1.01840193 -0.5258171064 -0.3862781611 -0.631526388
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## [214,] -1.433696923  0.30117834 -1.1167790798  0.7158629306  0.010513237
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## [220,]  4.811125983  2.34468196 -0.3322754239  0.5855998508  1.125323479
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## [275,]  0.329127497 -0.70211196 -1.1270499206 -1.3794822582  0.788719121
## [276,] -1.859016837 -0.41444458 -1.0884680056  0.0004891493  0.032889030
## [277,]  2.011187895 -1.86028031 -1.4701740451  1.9592818340 -0.863881329
## [278,]  4.387657320  1.01990704 -1.0694317529  1.0313056985  0.910287718
## [279,] -1.562200265  0.50506920  0.3257902808  0.4071536855 -1.418071805
## [280,]  1.140064695 -0.84165314  0.0475366423  0.1828157194 -1.383731574
## [281,] -1.592089421  0.68980851  0.0241838972 -0.0763303675 -0.781020214
## [282,] -0.863852065  0.20642081 -0.8983962803 -1.0667886017  0.713765183
## [283,]  1.027169030  1.16456255 -1.0404846287 -0.0396471898  1.049317709
## [284,] -0.436517354 -0.42713213  0.0134409058 -0.8973018413 -0.722139204
## [285,]  0.337411799 -0.24417082 -0.6480989722 -0.0855047074 -0.227110796
## [286,]  0.922063650 -0.22614793 -1.9443047687  0.7895315305  1.017821370
## [287,]  0.074518204  0.02674638 -1.0857966267  0.5553685803  0.035340926
## [288,]  0.517903752  0.07720678  0.7802091323 -0.3889323964 -1.326401252
## [289,]  1.205633993  4.05992941  1.7774871852  0.5243784073 -0.779237256
## [290,]  5.667322803  1.41683162  0.5192606886 -0.5242010735  0.057913957
## [291,]  0.117634314  2.05280704  1.1202906141 -0.2225732744 -1.394044856
## [292,] -1.257776898  0.99085451 -0.6432249171  0.7239870280 -0.267413061
## [293,] -1.442594978  0.64860803 -1.1825132672  1.3464166771 -0.103965971
## [294,]  0.581815447  0.15948370  0.5111637426 -1.5852378542 -0.514462082
## [295,]  3.192976367 -0.80514579  0.6934590185 -0.6145019682 -1.279398203
## [296,] -1.664428065  0.44940153 -0.8138817842  0.9169350091 -0.409961580
## [297,] -1.381280799 -1.04718836 -0.8104653996 -1.2130194950  0.131190811
## [298,] -0.359580844 -0.02707621 -0.2139147820  0.7519546558 -1.081305483
## [299,] -1.295214100  0.90633579  0.3446284016 -0.9705650257 -0.587847432
## [300,]  1.275367360 -0.46955884 -0.9321790556  1.6880185073 -0.857351331
## [301,]  0.510190648 -0.47545309  0.1659852525 -1.4398287570 -0.586650046
## [302,]  0.497692443  0.73632621 -0.7320867366 -0.6396358886  0.543145415
## [303,] -0.360524908  1.94049135 -0.0814679929 -1.0578009624  0.492777950
## [304,]  0.680162177  4.39853961  1.3939873156 -0.0903894719 -0.359689359
## [305,]  0.651993920  1.46566547 -0.5054646735  1.4206026417 -0.393377040
## [306,]  3.788964776 -1.08829199 -1.2835697130  1.5189289232 -0.160003180
## [307,]  0.324102302  0.44636919 -0.0358560470 -1.7147746806  0.185602167
## [308,]  1.241627938 -0.80113200 -0.9370602561  0.5736384332 -0.380036721
## [309,] -0.511968929 -1.17458566 -0.6546640582 -0.3823368294 -0.528559592
## [310,]  0.718039754  0.17733890 -0.6884966946 -1.2988653722  0.666658316
## [311,] -0.310163020 -1.06311682 -0.8411613032 -0.3440185709 -0.239649145
## [312,] -1.033055205  1.28803157 -0.7885399882  1.0583019502 -0.014148637
## [313,] -0.764852259  0.84975776 -0.4166580478 -0.3570104900  0.163850456
## [314,]  2.840965510  1.27703956  1.2737033558 -0.0712572107 -1.299150219
## [315,] -1.178758036 -0.07789715 -0.1547232721 -1.1892312531 -0.258297637
## [316,] -0.802177079 -0.95036649 -0.6926590212  0.0641135168 -0.653215774
## [317,]  1.938258838 -1.28408318 -0.7550485265 -0.2456973992 -0.386044302
## [318,] -1.084340607  0.56509571 -0.3641566428 -0.4657496728 -0.069947785
## [319,]  5.007927517  1.33213703  0.4628978606 -0.6412930066  0.335503981
## [320,] -0.352175349  0.05184295 -1.0595996323  1.1419351290 -0.354514092
## [321,] -1.645893870  0.67772347  0.5678664419 -0.6516041624 -1.130232840
## [322,] -0.723629619  0.28418574 -0.9155428645 -1.7398043966  1.090294733
## [323,]  2.150497872 -1.85335253 -0.9536747162 -0.9930159522  0.090967074
## [324,]  0.219479185  0.70653560  0.4625353948  0.0635989317 -1.095438714
## [325,] -0.347437994  0.13601327 -0.3616040070  0.0995137840 -0.602584780
## [326,] -0.234908136  0.38370796  0.3810829977  0.2955102824 -1.313248723
## [327,]  0.016559745 -0.24813137  0.3418529439 -0.6289931873 -1.073354029
## [328,] -1.467247701 -0.93657939 -1.0073778050 -1.3484920808  0.464904725
## [329,]  1.154836707 -1.65839860 -0.1796696786  0.5786916927 -1.773817068
## [330,]  0.020892606  0.14389944  0.1408600742  0.1842691926 -0.953519579
## [331,]  0.169022729  0.24173475  0.6782816134 -1.3801420819 -0.971815989
## [332,]  0.596241854  0.70051500 -1.8052088015 -0.0053918173  1.465700551
## [333,] -1.658882001 -0.32657130  0.2318064743 -0.3636469103 -1.209182254
## [334,] -1.130296134  0.92484749 -0.3380519552 -0.3013039197 -0.112208131
## [335,] -0.114349001 -0.27920208 -0.6403335111 -0.2074405468 -0.257747260
## [336,] -1.180178802  0.03183833 -0.3500656477 -1.0972084429 -0.005358715
## [337,]  1.016962553 -1.84125842 -1.0359966156  0.1725787385 -0.567197423
## [338,]  1.874901202 -1.13532877 -0.6093993174  1.0930613053 -1.160229327
## [339,] -1.674481841  0.44986836  2.1646104925  0.9678148811  0.135461099
## [340,]  0.347838749 -0.88857174  0.8771393702 -0.0399280185  1.772672225
## [341,] -0.523787799 -0.92658682  1.5418929659  0.1325485002  0.785980424
## [342,] -1.191298001  1.23405600  1.7890495622  1.3692564275  0.892653715
## [343,]  1.808772263 -1.69685692  0.8907964331 -0.2029722962  1.489618576
## [344,] -1.770065768 -0.81617964  1.3539885104 -0.2766980579  1.166492368
## [345,] -0.206433118  0.56197089  1.8053747930  1.3814075643  0.495893161
## [346,]  0.781356058 -0.26730308  1.4981375832  0.8043655618  1.134248369
## [347,] -1.821829245 -1.41978625  1.5929954355 -0.6929508188  0.865846962
## [348,] -0.284787326 -0.98055909  2.0711730642 -0.3625595662  0.392274537
## [349,] -0.436832085  1.81979653  1.9654352950  0.0409412675  1.657960929
## [350,] -1.217940564 -0.03242505  1.5341269350  0.0689673368  1.157904466
## [351,]  1.408443279 -0.92755403  2.5527909101 -0.6932672647  0.150225917
## [352,]  0.076806137 -0.36230781  1.0569801425  0.7081503355  1.356282603
## [353,] -1.371613972 -0.73826316 -0.0390647200  0.5827617423  2.417181597
## [354,] -1.864312777 -1.17836386  1.6190160585 -0.8239266507  0.990897877
## [355,] -1.989259900 -1.78295952  1.5112558257 -0.6883823148  0.805384073
## [356,] -0.666931670  0.04442279  0.9603229118  1.9679277491  0.821582895
## [357,] -0.752021652  0.57932223  1.1919215542  0.0297044937  1.852331941
## [358,] -0.799705965 -1.07103612  0.3748144882  2.1390626788  1.010092176
## [359,] -1.601727166 -1.41026284  0.7915067164 -0.2584759327  1.601877583
## [360,] -1.657122757  0.50517962  1.7207936026  1.3778309508  0.405279647
## [361,] -0.384493964 -0.88081329  0.5179378168  0.9525680456  1.560400572
## [362,] -1.117824446  0.07013439  2.3329630062 -0.8981794794  0.738754653
## [363,]  2.156938592 -0.59054334  0.9679981313  1.4564801625  1.063503699
## [364,] -0.789754021 -2.12761614  1.4729430325  0.0219314842  0.410727684
## [365,] -1.380570918 -1.02926654  1.9974600705 -1.3875631548  0.968366183
## [366,] -1.291560292  0.38334086  1.4160677141  1.5258026469  0.762317564
## [367,] -0.935262338  0.56231264  2.1242791830  0.3720182728  0.718006182
## [368,]  2.492171120 -0.48928746  2.4676282836  1.9668068431 -0.727490529
## [369,] -0.327363502 -0.84626614  2.2688783371  0.9603180211 -0.407816836
## [370,] -1.468296601  0.18028669  1.6652393313  1.5773153771  0.412661443
## [371,]  0.644477407  1.35334644  2.6883609615  0.5712489712  0.440528158
## [372,]  4.369563022 -1.66481832  1.6865361527  0.4901972904  0.760040778
## [373,] -2.357052820 -1.26900605  1.5231357317  1.0301102498  0.074632682
## [374,]  0.718708019  0.22127710  1.0354060443  0.2583339391  1.891779073
## [375,]  1.391878059  0.98004221  1.7111474295 -0.7952838709  2.265775349
## [376,]  0.905097897 -0.22694710  2.1140189340  0.5476029310  0.603860387
## [377,]  3.157230391 -1.19754195  1.1484347290  1.0599855046  1.186962665
## [378,]  0.003135705 -0.90598915  1.6393299343 -1.1011824448  1.359035590
## [379,] -0.242056357 -0.73255189  1.7021620290 -0.1866470103  0.800865246
##                 PC6          PC7
##   [1,]  0.814428206 -0.107883916
##   [2,] -0.048912344 -0.099604504
##   [3,] -0.086507916 -0.138527863
##   [4,] -0.822748232  0.360506834
##   [5,] -0.108812986  0.078970882
##   [6,]  0.183797925  0.433343571
##   [7,]  0.008911379 -0.004657966
##   [8,]  0.543125568 -0.332707934
##   [9,] -0.752701863  0.056474342
##  [10,] -0.441826427 -1.924448799
##  [11,] -0.244944687  0.159851097
##  [12,]  0.206259597 -0.169273224
##  [13,]  0.163519054 -0.103667561
##  [14,]  0.132474346  0.108653816
##  [15,] -1.324055932 -0.183915616
##  [16,]  0.714919089  0.304537991
##  [17,] -0.647376538  0.365592105
##  [18,]  1.097596271 -0.377715183
##  [19,]  0.334391075 -0.234827285
##  [20,]  0.808587321 -0.200036177
##  [21,]  0.322170368 -0.166529357
##  [22,]  0.107803508  0.012805983
##  [23,] -0.332323319 -0.202474142
##  [24,]  0.995998868  0.201016672
##  [25,] -2.363493528  0.266625584
##  [26,] -0.813907073 -0.571488560
##  [27,] -2.160783056  0.281527887
##  [28,]  0.098479393  0.336756957
##  [29,]  0.004273460 -0.381406184
##  [30,] -0.044211599 -0.418300721
##  [31,] -0.128464996  0.054899611
##  [32,] -0.357344175  0.183909490
##  [33,] -0.597244606  0.289672968
##  [34,]  0.259235600  0.349194654
##  [35,] -0.236888897 -0.371166651
##  [36,] -0.249251785  0.050335461
##  [37,]  0.607590347 -0.462113845
##  [38,] -0.026797156  0.355817879
##  [39,]  0.166045669 -0.073826942
##  [40,] -0.162738506 -0.392300116
##  [41,] -0.522507663 -0.121724380
##  [42,]  0.067225848  0.209115377
##  [43,] -0.417780877 -0.474060203
##  [44,] -0.173878940 -0.457967209
##  [45,] -0.050403121 -0.134114068
##  [46,] -0.089979747 -0.491479393
##  [47,]  0.480573605 -0.072323181
##  [48,]  0.228887831  0.155522234
##  [49,] -0.489991807 -0.227097997
##  [50,] -0.606582969 -0.101166456
##  [51,]  0.577660866 -0.455756839
##  [52,]  0.585446120 -0.388137976
##  [53,]  0.734811073  1.561539615
##  [54,]  1.381511548  0.252947237
##  [55,]  0.358959045 -0.182311216
##  [56,]  0.207910788  0.078632864
##  [57,]  0.607774154 -0.281869942
##  [58,]  2.443161543  0.443513680
##  [59,]  0.206843192  0.253038172
##  [60,]  0.135499206  0.164773439
##  [61,]  0.648725932  0.351461678
##  [62,]  0.166486526  0.246682271
##  [63,] -0.513948300 -0.286040883
##  [64,]  1.163578265  0.263125274
##  [65,] -0.009862807  0.134046265
##  [66,] -0.730377136  0.337181681
##  [67,] -1.487448857 -0.149925371
##  [68,]  0.220853759  0.272493773
##  [69,] -0.588054260  0.260689981
##  [70,] -0.385273067  0.319508713
##  [71,] -0.175254751  1.897246402
##  [72,] -1.300330063 -0.404208363
##  [73,]  0.816322549 -0.225387244
##  [74,] -0.060212427  0.165026305
##  [75,] -1.649589162 -0.529795744
##  [76,]  0.569158827 -0.263377372
##  [77,] -0.165692949 -0.401192949
##  [78,]  0.043436354  0.440699177
##  [79,]  0.327782857  0.371732847
##  [80,]  0.016945132  0.140928440
##  [81,] -0.877693420 -0.271276638
##  [82,]  0.050656761  0.314869348
##  [83,]  0.024270266 -0.489647178
##  [84,] -0.428408376  0.144447332
##  [85,]  0.302353058  0.176709283
##  [86,] -0.930367776 -0.038966156
##  [87,]  0.206974359  1.518547012
##  [88,]  0.773220076  0.387655208
##  [89,] -0.057425863  0.311702214
##  [90,] -0.319492539 -0.104439493
##  [91,]  0.464021241 -0.182053564
##  [92,]  0.568469956  0.135273025
##  [93,] -0.637098352 -0.352179961
##  [94,] -0.897710356 -0.603436508
##  [95,] -0.302718373  0.134220300
##  [96,]  0.796303291 -0.453234619
##  [97,]  0.102248374 -0.373850042
##  [98,]  0.276775028 -0.386841666
##  [99,] -0.147547074 -2.150145655
## [100,]  0.522935395 -0.336156710
## [101,] -1.015284422 -0.131608533
## [102,]  0.945355253  0.288290374
## [103,]  0.240503118  0.089283023
## [104,]  0.040655927 -0.326527188
## [105,]  0.156719385 -0.425753859
## [106,] -0.378077108 -0.375663969
## [107,]  0.617517671 -0.018331347
## [108,] -0.140360458  0.357139007
## [109,] -0.369058053 -0.363453154
## [110,]  1.367651547 -0.052494633
## [111,] -0.245674045  0.171961839
## [112,] -0.288279169 -0.437854120
## [113,]  0.654181743  0.335734007
## [114,]  0.430171258  0.242838061
## [115,] -0.609725681 -0.399796060
## [116,] -0.153071461  0.293451739
## [117,]  0.435961104  0.348338090
## [118,] -1.122876095  0.371334968
## [119,]  0.128953459 -0.002950892
## [120,]  0.454338848 -0.320002000
## [121,] -0.393321862  0.002244332
## [122,]  0.694427666 -1.776651924
## [123,] -1.480360092  0.237363812
## [124,]  0.563305776  0.061168635
## [125,]  0.789672355  0.182676841
## [126,]  0.657430786  0.151394277
## [127,]  0.052053042 -0.260063201
## [128,] -0.509971776  0.300299579
## [129,] -0.514688913  0.253498821
## [130,] -0.230653718  0.334001823
## [131,]  0.234492897  0.070164155
## [132,] -0.509623760  0.211476411
## [133,] -0.508032972  0.218820879
## [134,] -0.584676128  0.432040803
## [135,] -0.599512631  0.114578050
## [136,]  0.742555446  0.264941606
## [137,]  0.215593238 -0.296341138
## [138,]  0.814373445 -0.463329220
## [139,] -0.705236433  0.235224585
## [140,] -0.240819937  0.128832004
## [141,] -0.738265473  0.045748305
## [142,] -0.516065685  0.423763629
## [143,]  1.032627703  0.255695270
## [144,]  1.011640901 -0.046612704
## [145,]  1.036057364 -0.116502648
## [146,]  0.238779557 -0.094409829
## [147,]  0.093045275 -0.025943269
## [148,] -0.018285774  0.063985702
## [149,] -0.821062597  0.316957388
## [150,] -0.051433159 -0.325889337
## [151,]  0.240258258  0.157499206
## [152,]  0.244055313 -0.484326189
## [153,]  0.321762278  0.347844280
## [154,] -0.688031620  0.275674116
## [155,]  0.052870105  0.278750325
## [156,]  0.259394959  0.994613529
## [157,]  0.384573263  0.255112420
## [158,] -0.647167228  0.095523521
## [159,] -0.447355557 -0.367626528
## [160,] -1.037268876 -0.081314104
## [161,]  0.685349399 -0.373379228
## [162,] -0.574402441 -0.041182433
## [163,] -0.812645636  0.354791023
## [164,]  0.259528832  0.196856471
## [165,] -0.112837907 -0.422270866
## [166,]  0.128000241 -0.175939627
## [167,] -0.895512404  0.337192272
## [168,] -0.711019273 -0.814804273
## [169,]  0.218357219 -0.033915231
## [170,] -0.078144315  0.263676922
## [171,]  0.789052948  0.069697557
## [172,]  0.334044498  0.095799549
## [173,] -0.466799910  0.182242801
## [174,] -0.409218588  0.105315011
## [175,]  0.475675622  0.157100174
## [176,]  0.631970192 -0.312887516
## [177,] -0.842796008  0.184336624
## [178,] -0.521271064  0.253595738
## [179,] -0.195535437 -0.489681481
## [180,] -0.238968439  0.339455192
## [181,]  1.224469205  0.162311433
## [182,]  0.896759582 -0.187133556
## [183,] -0.369525579  0.051355060
## [184,] -1.133798661 -0.032484936
## [185,] -0.525703790  0.938668397
## [186,]  0.115704613 -0.308573611
## [187,] -0.330011041  0.052298230
## [188,]  0.252831722 -0.344500770
## [189,]  0.478267892 -0.411989559
## [190,]  0.108389410  0.270176494
## [191,]  0.320051815 -0.452948617
## [192,] -0.927317654  0.050049377
## [193,]  0.049967323  0.232020283
## [194,] -0.322439393 -0.332013839
## [195,] -0.576452643  0.112196595
## [196,] -0.426323754  0.064708147
## [197,]  0.577314293 -0.090994712
## [198,] -0.220002645 -0.145293651
## [199,]  1.007924154 -0.238873759
## [200,] -0.144916255 -0.256657796
## [201,]  0.222523935 -0.327353336
## [202,]  0.143637470 -0.384469784
## [203,] -0.685873899  0.077706170
## [204,] -0.684433914 -0.555287379
## [205,] -0.739601209  0.286336764
## [206,] -0.391145161  0.071275723
## [207,]  1.031184262 -0.071523474
## [208,]  0.422795216 -0.361912372
## [209,]  0.232252275 -0.321891385
## [210,]  0.132512399 -2.194006418
## [211,]  0.300407101  0.236278993
## [212,] -0.181056517 -0.655811887
## [213,] -2.264161275  0.013076856
## [214,] -0.146543860  0.258375350
## [215,] -0.914443039 -0.156858207
## [216,]  0.163052914  0.373094641
## [217,]  0.735902331  0.298434341
## [218,]  0.858016687 -0.410620478
## [219,] -0.698483214  0.291328307
## [220,] -1.702108557 -0.103054608
## [221,] -0.570947694 -0.064210529
## [222,]  0.103014117 -0.154551366
## [223,]  0.032313480  0.248280548
## [224,] -0.245512705 -0.395034205
## [225,] -0.795643311  0.316447811
## [226,]  0.757677018  0.355289619
## [227,]  0.112343498 -0.370694673
## [228,]  2.840081863 -0.472760040
## [229,] -0.117535015  0.251369052
## [230,] -0.123999729 -0.103219333
## [231,]  0.620151206 -0.398726087
## [232,] -1.258499518  0.031686285
## [233,]  0.508788077  0.031702502
## [234,] -0.730990134  0.229897436
## [235,] -0.131943879  0.351750927
## [236,]  0.930178961  0.218030323
## [237,] -1.155883577 -0.406938969
## [238,]  0.421016873 -0.245001577
## [239,] -0.919968833  0.339656927
## [240,] -0.475488496  0.136247856
## [241,]  1.761754259  0.029538972
## [242,]  1.222218060 -0.319429458
## [243,] -0.387563364 -0.168870331
## [244,] -1.348003518 -0.078702906
## [245,] -0.096908019  0.116533237
## [246,]  0.123274608  0.151123503
## [247,] -0.489960306  0.098338159
## [248,]  0.676566199 -0.339944716
## [249,]  0.072286130  0.262572292
## [250,] -0.203974262  0.359934672
## [251,] -0.962511140  0.447744836
## [252,]  0.026617023  0.293556296
## [253,] -0.615601226 -0.158798853
## [254,]  0.165313198  0.013008846
## [255,]  1.432136191  1.223639292
## [256,]  0.483977624 -0.346520349
## [257,] -0.153805545  0.159416002
## [258,] -0.327177547  0.145372443
## [259,]  0.927279628  0.136024542
## [260,]  0.347645497 -0.209884830
## [261,]  0.229700925 -0.104543344
## [262,] -0.158104523 -0.333049945
## [263,] -0.057284357 -0.187261115
## [264,] -1.002026891  0.117204649
## [265,]  1.233710972  0.172803485
## [266,] -0.621049559 -0.266818669
## [267,]  1.556396291  0.244375096
## [268,] -0.067622566 -0.072725103
## [269,] -0.175077307 -0.498801012
## [270,] -0.666813685  0.155867363
## [271,] -0.136040334 -0.327359471
## [272,]  0.778990215 -0.465309183
## [273,]  0.693723928 -0.130197667
## [274,] -1.468695169  0.266972231
## [275,]  0.429361577 -0.105547847
## [276,] -0.773390730 -0.033260132
## [277,]  0.336674762  1.064820895
## [278,] -0.300804152  0.703841870
## [279,] -0.238262975  0.450690335
## [280,]  0.395969716 -0.242043012
## [281,]  0.109021256  0.138748544
## [282,] -0.037963898  0.268885486
## [283,] -0.373873694 -0.512209208
## [284,] -0.029714459 -0.403875221
## [285,]  0.426625104  0.228719436
## [286,] -0.362288537  0.223311049
## [287,]  0.384277844 -0.106878993
## [288,] -1.421668738  0.046595855
## [289,] -2.984199195  0.075859453
## [290,]  1.319916883  2.001667923
## [291,]  2.046793198 -0.269649215
## [292,]  0.392813424  0.303644436
## [293,]  0.021688217  0.270137554
## [294,] -0.049144987 -0.046060227
## [295,] -1.011855498 -0.955345258
## [296,] -0.175912153  0.163389864
## [297,] -0.811118093  0.416648260
## [298,] -0.340865035 -0.224224889
## [299,]  0.466059600  0.157785884
## [300,]  0.558304051 -0.192471657
## [301,]  0.750653613  0.459663166
## [302,]  1.122352945 -0.276052847
## [303,]  1.078964668  0.210264826
## [304,]  0.426300512  0.141513828
## [305,]  0.810547774  0.065859782
## [306,] -0.181814543  1.697357273
## [307,]  0.699571022 -0.449062901
## [308,]  0.145047367 -0.510569761
## [309,] -0.335948519 -0.163889426
## [310,]  0.695110312 -0.089730044
## [311,] -0.421019920 -0.164631917
## [312,] -0.328893323  0.125575320
## [313,] -0.600269847  0.190331629
## [314,] -0.800239413 -0.264240505
## [315,] -0.079057717  0.438769076
## [316,] -0.386407008 -0.406110560
## [317,]  1.041640267  0.390303651
## [318,] -0.189857024  0.234508553
## [319,] -1.090183460  0.762300322
## [320,]  0.386282802 -0.239807387
## [321,]  0.134404520  0.127105246
## [322,]  0.366835108  0.216268360
## [323,]  0.342909111  0.372677157
## [324,] -0.254516438 -0.193658003
## [325,]  0.533845103 -0.328861238
## [326,] -0.465612342 -0.352871158
## [327,] -0.163023346  0.003333250
## [328,] -0.798713796  0.164392019
## [329,]  0.481838526 -1.448359073
## [330,] -1.226111979 -0.366016068
## [331,]  1.020308661  0.044230674
## [332,]  1.056394345 -0.394589336
## [333,] -1.007313550  0.374213944
## [334,]  0.492601789  0.244276984
## [335,]  0.411613111 -0.135788109
## [336,] -0.280767946  0.263720304
## [337,]  0.160862506 -0.192753984
## [338,]  0.791036742  0.678047807
## [339,]  0.126529280  0.120748763
## [340,]  0.262317102 -0.088849352
## [341,]  0.041119374 -0.483927739
## [342,] -0.678266870 -0.258446039
## [343,]  1.445310485  0.036985630
## [344,] -0.175915279  0.027902348
## [345,]  0.564004554 -0.503273137
## [346,] -1.123890798 -0.049820336
## [347,] -0.529962184  0.213624141
## [348,]  0.448319463 -0.109057231
## [349,]  0.164185074 -0.178027089
## [350,]  0.343302649  0.295711308
## [351,]  1.064600476 -0.399557062
## [352,]  0.402428026 -0.264910522
## [353,] -0.039235833  0.080955691
## [354,] -0.401278508  0.033682397
## [355,] -0.845062983  0.190359077
## [356,]  0.916027349 -0.545821754
## [357,]  0.946629462  0.303161216
## [358,] -0.119192699 -0.421977595
## [359,] -0.474603729  0.232244290
## [360,]  0.620269650  0.217072532
## [361,]  0.290272477 -0.446292100
## [362,]  0.807055770  0.427223893
## [363,]  1.725250067  0.275888197
## [364,] -0.573212533 -0.177662617
## [365,] -0.242829260  0.310782840
## [366,] -0.025556816  0.310309937
## [367,] -0.369535370  0.246732337
## [368,]  0.794924538  0.929445109
## [369,] -0.044906053  0.144701045
## [370,] -0.730353345  0.202922032
## [371,]  0.105639703 -0.429239913
## [372,] -0.245135971  0.186120856
## [373,] -0.823120736  0.174853047
## [374,]  1.126518713 -0.084801083
## [375,] -0.200011773 -0.549385252
## [376,] -1.229143214  0.135743929
## [377,] -0.299503313  0.743333133
## [378,]  0.410392839 -0.361555114
## [379,]  0.837670932 -0.196874004
# Identifying the scores by their survival status
sparrtyp_pca <- cbind(data.frame(Cancer$Survivor),Cancer_pca$x)
sparrtyp_pca
##     Cancer.Survivor          PC1         PC2           PC3           PC4
## 1             Alive -1.441559363  1.84595445 -0.3691842456  0.8313546497
## 2             Alive  0.466697152  0.06803649 -0.6236808487 -0.3679040103
## 3             Alive  1.724644704 -0.46933933 -0.1593826887  0.5351088884
## 4             Alive -1.727412749 -0.67153366 -0.6471303735 -0.0657071859
## 5             Alive  0.084534880 -1.24252757 -1.5702796993 -0.3040439925
## 6             Alive -0.987174108  0.58301426  0.1669091720 -0.9999683133
## 7             Alive -1.289312885  0.33343114 -1.1225709379 -0.4660831193
## 8              Dead  0.457476281 -0.43703336 -2.3348237400 -0.5798103154
## 9             Alive  5.013544810 -0.35127563  0.3138865965 -0.6789485742
## 10            Alive  1.966110970  0.57900951  0.8436785098  1.1971488330
## 11             Dead -1.709742154  0.39272616 -0.8797546127  1.0395229446
## 12            Alive  1.323214712 -1.40692828  0.0010448762 -0.8532983622
## 13            Alive -0.047344848  0.20982069 -0.8615166802  1.1288786920
## 14            Alive -0.023379894  1.83512622 -0.8543600804 -0.5919635549
## 15            Alive  1.042993427  1.19479846 -0.1106365956  0.7578922926
## 16            Alive -0.954171084  1.25373181 -0.8631921253  0.4922727293
## 17            Alive -0.510183493 -1.74284660 -0.1083044907 -0.2184460954
## 18            Alive  0.248390384  0.43156365 -0.4623851738 -1.2333483190
## 19            Alive -0.386424810 -0.37494859  0.5477775527 -1.3442739171
## 20            Alive -0.212235416  0.44848661 -0.0814638947  0.1978257208
## 21            Alive  0.001291199 -0.22401731 -0.1753398416 -0.9042251252
## 22            Alive  0.547237523  0.35323566 -0.8945832960  0.4857434118
## 23            Alive -0.581794885 -1.07033107 -0.7283097731 -0.0629010628
## 24            Alive  1.484574719 -1.12275223  0.4930197218 -0.8534326311
## 25            Alive  0.730385134  3.01009366  1.5328340955 -0.0845516282
## 26            Alive  1.384044724  2.86730858  0.7935319092  0.4879719811
## 27            Alive  2.503197607  1.86942247  1.6035708576 -1.0898911376
## 28            Alive -1.094732396  0.13919430 -0.2430526831 -1.3348711724
## 29            Alive -0.040233637  0.24894946 -0.5823916977  0.1870202613
## 30            Alive -0.913495245 -0.27255918 -0.2249052502  0.7136559763
## 31            Alive  0.044817272 -1.24749459 -1.5147400984 -0.3403352312
## 32            Alive -1.310023914 -0.18810081 -1.5041631045 -0.0748728835
## 33            Alive -1.750326793 -0.31441971 -0.3126381565 -0.1365620557
## 34            Alive -0.860691537  1.17774354 -0.4731321013  0.2383866081
## 35            Alive  1.293140200  1.12837700 -1.0955034983 -0.3513923420
## 36            Alive -1.575412171 -0.65517742  1.1178980897 -0.0145585733
## 37            Alive  0.505620687  0.48204717  0.6768751198  0.9826148200
## 38            Alive -1.445729993 -0.53420180  2.0397881463 -0.4191403509
## 39            Alive -0.240634131 -1.38008841  1.2981310791  0.0234566336
## 40            Alive -0.335231355 -0.71567154  2.2622815166 -0.2598837684
## 41             Dead  2.392046521 -0.75381886  0.6808155988  1.7849935943
## 42            Alive -1.496209472 -0.05147919  0.8362058172  1.4463882147
## 43            Alive -1.238156754 -1.73396163  1.0838915624  1.1966166369
## 44            Alive -0.122858339 -0.41520397  1.7259286489  0.2467343049
## 45            Alive -1.614959830 -0.21262796  0.8270352673  0.5084458503
## 46            Alive  0.653344872 -1.45282335  1.6923961454  1.7730389364
## 47             Dead -0.903132282  0.00288121  0.2891894480 -0.3828977838
## 48            Alive -1.570956435 -0.13307164  0.7378711359  1.2691205943
## 49            Alive  0.407142180 -0.18484286  1.8224576827  0.3406571927
## 50            Alive -2.095133885 -0.24603762  1.3075254314  1.5865972660
## 51            Alive  0.145196356 -0.72051716  1.2885099274 -1.1072761596
## 52            Alive  0.438754344 -1.67207421  0.9831353778  2.3512915236
## 53            Alive  2.005777230 -2.95342227  1.2688959631  1.7356814675
## 54            Alive  1.526981600 -1.02119752  1.4223445513  1.8001650835
## 55            Alive -1.762004433  0.13389155  1.3060891880  0.4365138287
## 56            Alive -1.584099552 -0.27233552  1.1461680461  0.3643457178
## 57            Alive -0.496130040  0.33490544  0.2711418287  0.1648088615
## 58            Alive -0.310631363  3.07311289  1.8743230894 -1.7983452746
## 59            Alive -1.133478035  0.41599332 -0.4379284603 -0.8528069490
## 60            Alive -1.203472671  0.78226143 -0.1914939617 -0.4844823758
## 61            Alive -0.899762531  1.31926126  0.1811318594 -0.4938217806
## 62            Alive -1.006446958  0.35539993 -1.2221294160 -0.3469217710
## 63            Alive -0.437812701 -1.58636590 -0.8897438306 -1.2595916576
## 64            Alive  1.712300783 -0.45593265 -0.1013381728  0.5911078860
## 65             Dead -1.263885916  1.17224839 -0.6291534095  0.9206949813
## 66            Alive -1.604219653 -0.82712464  0.0494208809 -1.5797529143
## 67             Dead  4.488026052  1.14176192 -0.1231038156 -1.5112898673
## 68            Alive -0.665172931  0.68451038  0.1453995807 -2.0258292592
## 69            Alive -1.668377900 -0.33091730 -0.6606673180 -0.0526400595
## 70            Alive -1.130422629  0.23695569 -0.1769384999 -0.7612337767
## 71            Alive  3.316812797 -1.81535426  0.5502180418 -0.2694003925
## 72             Dead  2.172380940  2.85911092 -0.9844345887  1.6403461146
## 73            Alive  0.572326326 -0.34757898 -1.0234096521 -2.0869344002
## 74            Alive -1.827615023  0.62057292  0.3016558087  0.2426806849
## 75            Alive  0.720276568  1.70219107  0.6872975038  0.8005007414
## 76            Alive  0.849193077 -1.14260361  0.1217975270 -0.0272015985
## 77            Alive -0.640547040 -0.61272303  1.3854969929  1.5959470836
## 78            Alive -0.095120639 -2.25942107  1.7743414136 -0.8570595769
## 79            Alive -0.045215749 -1.67214619  1.1930256589  0.3311124134
## 80            Alive -1.769164273 -0.22777378  0.5215512977  1.9330657865
## 81            Alive  0.718379560  0.42702578  2.7049430509  0.0009902972
## 82            Alive -1.678008963 -0.30727716  0.8345249461  1.7090923528
## 83            Alive -0.895860760 -0.84819969  1.0351097886  1.6955225348
## 84            Alive -1.627068924 -1.17405222  0.1883777552  0.6241466387
## 85            Alive -1.331489281 -0.34160016  0.9121167916  0.1344506975
## 86            Alive  0.909892498 -0.53731582  1.4060161653 -0.0311065615
## 87            Alive  2.680823986 -2.87516871  1.2736995009  0.6959415006
## 88            Alive  1.353531002 -2.37316783  1.3254482077  0.7127875562
## 89            Alive -1.678967186 -0.70552936  1.6695940259  0.1038284595
## 90            Alive -2.304099591 -0.48981820  1.6210427235  0.9780934643
## 91             Dead  0.741204117 -2.34543537  1.4452706433  0.5998522096
## 92            Alive -0.809147683 -0.48805441  0.7203787577 -1.4686194537
## 93             Dead -0.790428226 -1.28394744  1.3498973595  1.2856985141
## 94             Dead  1.549314451  1.05942412  1.1109895492  0.1457696503
## 95            Alive -1.647991336 -0.27927996  1.6891990873  0.5048525410
## 96            Alive -0.268121798 -0.13194343  0.7385162603  1.3684964706
## 97             Dead -0.103534223 -1.33945241 -0.5191543874  1.0167737783
## 98            Alive -0.776307350 -0.99454099  1.0504553950  1.2109563269
## 99             Dead  1.103113756 -1.77799849 -1.0931648334 -0.0122323381
## 100           Alive -0.409442426  0.35492707 -1.0502000077  1.4204609639
## 101            Dead  4.633190126  2.16526818  0.6239105977 -1.1366907435
## 102           Alive -0.740349810  1.21149156 -0.0348952140 -1.2669488699
## 103           Alive  0.704221402 -1.11279489 -2.7553374907 -0.4028612238
## 104            Dead -0.385204834 -0.52764189 -1.2886177272  0.4419425766
## 105           Alive -0.068793640  0.07508422 -0.6067830446 -0.3162015548
## 106           Alive -0.692576410 -0.91636560 -1.3471231484  0.7054513599
## 107            Dead  0.345220609 -0.15476507 -1.9375149484  0.6213467649
## 108           Alive -1.364096376  0.64909093 -0.7204212843  1.0498159217
## 109           Alive -0.387521866 -1.16290394  0.1995560232 -2.1751452860
## 110           Alive  0.491580932  1.59726077 -0.0288299149  0.6365139827
## 111           Alive -1.087373932  0.96622658 -0.4850478973  0.2957151405
## 112            Dead  1.210180885 -2.10091879 -0.7122063654 -1.4443151802
## 113           Alive  1.869006469  1.83583553  0.7046224722 -1.0701872221
## 114           Alive  0.492734252 -0.45633393 -0.5614007104 -0.8951702764
## 115           Alive  0.889433533 -1.50731469  0.2004002058 -0.2364464439
## 116           Alive -0.849321798  0.50645649 -1.0584322308 -0.1780669707
## 117           Alive  1.382626614 -1.86070361 -0.1224339395 -0.3673855944
## 118           Alive -0.876114257  1.31244321  0.5402724456  0.6865577157
## 119           Alive  0.129510618 -0.29073195  0.1371234823 -1.0140234437
## 120           Alive  0.006142764  0.12672993 -0.8224846986 -0.0976817279
## 121           Alive -0.669636518 -0.67017693 -0.0910644210  0.8278709329
## 122           Alive  1.757579745 -1.15217572 -0.1806146788 -1.0023054945
## 123           Alive  1.875711497  0.92049908 -0.1305383937 -0.2267912179
## 124           Alive  0.312604564  0.73821191  0.3983729256  0.0063600881
## 125           Alive -0.681074580  1.46363098 -0.7243706847 -0.3192569625
## 126            Dead -0.863182056  1.24685123 -1.9912585523  1.1497711812
## 127           Alive -0.118572831 -0.70053670  0.2417380654 -2.0356708316
## 128           Alive -1.423953866 -0.28566927 -1.5423434161  0.5267774639
## 129           Alive -1.441335172 -0.03524627 -0.5051970790 -0.2755060729
## 130           Alive -0.856545337  0.21574546 -0.3501704930 -1.3208020069
## 131           Alive -1.307398005  0.79423090 -1.0835136941  0.4150931199
## 132           Alive  0.585398503 -0.41679342 -0.4499848326 -0.4042504411
## 133           Alive -1.786207788 -0.17673804 -0.0665424655 -0.3670738391
## 134           Alive -1.427017695 -0.63688709 -0.4649731902 -0.8892591027
## 135            Dead  0.756062138 -0.13112369 -1.3636990615  0.5752861401
## 136            Dead  0.145449916  1.69976295 -0.3153802001 -1.9246355296
## 137           Alive -0.274324587 -0.57433529 -0.2583518619 -1.1336704462
## 138            Dead -0.438129117  0.74050108 -0.3404267839  0.7633673055
## 139            Dead  1.064299809  0.61136855 -0.6550235320  0.9211144934
## 140           Alive  2.098096298 -0.42706015  0.8620866598 -0.4563567888
## 141           Alive -1.849943605 -0.47094945 -0.5180573283 -0.5701157634
## 142           Alive -0.732556857 -0.13070679  0.3510392562 -2.5238550573
## 143           Alive -0.608595125  1.35155467 -0.7057542462 -0.7165766057
## 144            Dead  0.505611656  1.09999711 -0.8457725436  0.9361832967
## 145            Dead  0.247551976  0.46673882 -0.7913160371  0.0399880240
## 146           Alive -0.602802743 -0.23260921  0.5437161698 -0.0788003168
## 147           Alive -1.272341157  0.63788399  0.2396679916 -1.6177473606
## 148            Dead  2.651497970 -0.83742214 -0.8602918415 -0.9187276925
## 149           Alive -1.824221268 -0.45358497 -1.0788845841  0.9216453730
## 150           Alive -0.352147008 -0.02439510 -0.1582340020  0.1140579142
## 151           Alive -1.129437762  0.24550127  0.4252415970 -2.4757263934
## 152           Alive -0.549974224  0.36383145 -0.6269521199  1.0856493132
## 153            Dead -1.104925141  0.73145555 -0.9068622646  0.3853904201
## 154           Alive -1.260493668  0.67356911  0.3950426508 -0.1537212632
## 155           Alive -1.263788087  0.89343258 -0.8613170835  1.0342322348
## 156           Alive  2.182293451 -0.70621431  0.3489551723  1.5351765574
## 157           Alive -0.839030427  0.51161725 -1.0551051340 -0.7935641661
## 158           Alive -1.567211240 -0.76592187 -0.0382695651 -2.2426462201
## 159           Alive -0.656681669 -1.17053344 -1.0085651375 -0.1509452878
## 160            Dead  1.746317858  1.20029090 -1.6249506696  0.9407644883
## 161           Alive  0.576848393  1.03248254 -1.8769456788  1.1403757019
## 162           Alive -1.591129974 -0.30100995 -1.4737482868 -0.1586928611
## 163           Alive -1.734769097 -0.63230165 -0.6993991424  0.0578306174
## 164           Alive -1.257058960  0.98743371  0.2695795040 -0.5173988569
## 165           Alive  0.171012852  0.73662045 -0.6335336460  0.6662455703
## 166           Alive  0.763873736 -1.48595671 -1.3893183822  1.8933152957
## 167           Alive -0.648233872  0.65902369 -0.3523707692 -0.3496173059
## 168           Alive  4.075761272 -0.02211354  1.3258187920 -1.7139363992
## 169           Alive  0.108096807 -0.74362678 -1.3323697664 -0.3209218040
## 170           Alive -1.498040609  0.19056435  0.2761281170 -0.9725452192
## 171            Dead  0.047885996  0.72229011 -0.4345521427  1.3431830404
## 172           Alive  1.337596168 -0.99890019 -0.4764831468  1.0952509419
## 173           Alive -1.358485537 -0.11022223 -0.3457867052 -1.0397848770
## 174           Alive -1.872027381  0.13432597 -0.2581474106  0.2022369490
## 175           Alive -1.311243234  1.36865781  0.6373415177 -0.4090917149
## 176           Alive  1.309706033 -1.47375458 -0.5852915698 -1.0931889293
## 177            Dead -0.190859319  1.67724390 -0.7080844449  0.4280689948
## 178           Alive -1.150520519 -0.39541176 -0.6403158755 -1.4507416448
## 179           Alive  1.562083350  2.47954880  0.2323943105 -0.3200123444
## 180            Dead  0.457663612 -0.14582329 -0.6638729701  0.7733241568
## 181           Alive -1.138195339  2.01560621  0.8465374351 -0.4823983801
## 182            Dead -0.007740653  0.82444862 -0.0002346095  0.3074323320
## 183            Dead -1.442466409  0.10416344 -2.2744315999  1.2646597948
## 184           Alive  1.401099127  0.69145106 -0.3432001965 -0.4552169029
## 185           Alive  3.044609211 -0.84163842  0.2359688651 -0.0030339038
## 186           Alive -0.608848019  0.10718396 -0.0234540132  0.6904571295
## 187           Alive  0.869481448 -1.63077965 -0.5698543214  1.5434401088
## 188           Alive -0.300778748  0.05603470 -0.4615545760  0.1636332520
## 189            Dead  0.636747830  2.30234603  1.1644239379  0.0093990323
## 190           Alive -1.117892469  0.18858115 -0.3253204166 -1.3032488160
## 191           Alive -0.433517740 -0.06760578 -0.8846842302  0.3292279071
## 192           Alive -2.074508151 -0.53753951 -0.4998051808 -0.0243119417
## 193           Alive -0.943857160  1.31427799 -0.3177697220  0.3467708448
## 194           Alive -0.671437346 -1.01840193 -0.5258171064 -0.3862781611
## 195           Alive  3.146400023 -0.15766658 -0.4540461596 -0.5782133325
## 196           Alive -1.646968799  0.07418381 -1.4456195095  0.8218169329
## 197           Alive  0.194381857  0.17982364 -0.8329361597  0.1578319644
## 198           Alive  1.355794604 -1.31217975  0.2126240281 -0.5341546811
## 199           Alive  0.342080981  0.71442970 -0.6482593800 -0.2099015734
## 200           Alive -0.390007297 -0.72256040  0.2659366383 -1.3023370226
## 201           Alive -0.278709707 -0.06166132 -0.3047482694 -0.2069801581
## 202           Alive -0.042662340  0.49913934 -0.5186429497  0.4553285736
## 203            Dead -1.773111892 -0.17830822 -1.7400026462  1.2398085147
## 204            Dead  1.250439359  1.30927635 -1.2548155696  0.1212141597
## 205           Alive -1.763032603 -0.39026215 -1.0709293305  0.7285468245
## 206           Alive -1.734908122  0.22532626 -1.3096386361  1.1382811564
## 207           Alive -0.040455138  0.55449852  0.4573444687 -0.4218347821
## 208           Alive -0.686284826  0.13219155  0.6118547014 -0.2432679726
## 209           Alive -0.444359734 -0.28370817 -0.4495876614 -0.0769292704
## 210           Alive  0.691490501 -1.91894081 -0.1931803231 -0.7485897999
## 211           Alive  2.007551495 -1.38730232 -0.5519627527 -0.6174453995
## 212            Dead  2.980951104  0.35496999 -1.5634230702 -0.6219160971
## 213           Alive -0.051043670  1.76211010  1.2088357396 -1.1338711513
## 214           Alive -1.433696923  0.30117834 -1.1167790798  0.7158629306
## 215           Alive  0.663189426  0.17003794 -0.7914480913  0.1781148795
## 216            Dead  2.031410016 -1.22967790 -2.3061777513  2.1455817946
## 217            Dead  0.789603453 -0.46930287 -1.7356512834 -0.3692602528
## 218           Alive  0.673484381 -0.39280224  0.0473568504  1.1650225109
## 219           Alive -1.540903396 -0.09859304 -1.1167612805  0.8029841934
## 220            Dead  4.811125983  2.34468196 -0.3322754239  0.5855998508
## 221            Dead  2.960210184  0.25580109 -1.3532023514  1.1105279220
## 222            Dead  0.548555090  1.20673516 -0.5847280068  1.2403006951
## 223           Alive -1.203818787  0.41491335  0.6516018979 -1.7888960008
## 224           Alive -0.095903547 -0.65584776 -0.5358363119 -1.2541542670
## 225           Alive -1.447284264 -1.00724102 -0.6082703522 -1.5298781643
## 226           Alive -0.721456172  1.13787970  0.8467912909 -2.0802276689
## 227           Alive  2.040310983  0.43242568 -0.2461052925  0.7423873284
## 228           Alive  1.855207556  1.67633604  0.5148301396 -0.1260125667
## 229           Alive -1.362709085  0.28203522 -1.2055884775  0.5729921576
## 230           Alive -0.288896751  0.20730044  0.2845176632  0.6308919312
## 231           Alive -0.418601999  0.23532480  0.2238988269 -0.5027334058
## 232           Alive -1.163850583  0.68497750 -0.8821849871  0.8863377110
## 233           Alive  0.411132602  1.16486925 -0.3493614654  1.3942763398
## 234           Alive -1.693135796 -0.47771445 -1.0852001549  0.2466849979
## 235           Alive -1.469262447  0.58168692  0.2179103849  0.0730339108
## 236           Alive -1.241804213  1.79930936  0.0417415503  0.6900290082
## 237           Alive  3.689808324  1.67054618  0.2271980354 -0.1712036874
## 238           Alive  0.637785394 -1.18641596  0.3164064662  0.3364686684
## 239            Dead  6.741912903  1.29247340 -0.5420542885  0.4573219426
## 240           Alive -1.238593026 -0.23776840 -0.5949271348 -1.3969869040
## 241            Dead  0.823175506  1.06316740 -0.5254541417 -0.6645444043
## 242           Alive  0.046147404  1.10794300  0.9541899343 -1.0517974932
## 243           Alive -0.926653518 -0.47703938  0.3584883210  0.7483755808
## 244           Alive  1.642861658  0.76706108  0.4101327315 -1.6601340760
## 245           Alive  0.577872627 -0.27228218  0.0857683853 -1.3777634787
## 246           Alive -1.754825326  0.80791517  0.5577871077 -0.0676093662
## 247           Alive -2.038325012  0.13688760 -0.0003412363  0.3430358578
## 248            Dead  0.534102452  0.42078510 -1.1547081981 -0.6235503927
## 249           Alive -0.778602587  0.16187841 -0.3007337578 -2.1397103069
## 250           Alive -1.358620602 -0.11871598 -0.0786250759 -1.0668656351
## 251           Alive  0.552972231 -1.32892174  0.2653874378 -1.7448134449
## 252           Alive  0.160512695 -1.07401603 -1.3645629081  0.1229912862
## 253           Alive -0.255760964 -1.55052571 -0.6215940219 -1.4389507212
## 254           Alive  2.380048532 -1.22313608 -0.4828668231 -1.7734074221
## 255           Alive  2.562080786 -0.62564376 -0.7980444051  1.7530531164
## 256           Alive -0.556325503  0.61870762  0.4208116759  0.5833612102
## 257           Alive -1.361977024  0.48557037 -0.3780687286 -0.2263198361
## 258           Alive -1.604168388  0.15729081 -1.1427967214  0.6878894786
## 259           Alive  0.453544197 -0.10135935 -0.0830135546 -1.4480142567
## 260           Alive -0.245088734 -0.21116664 -0.8071754259  0.2429511311
## 261           Alive -0.586494355  0.59713665 -2.4100725243 -0.5973150226
## 262           Alive -0.595783004 -0.97017702  0.1712856607 -1.4091442191
## 263           Alive -0.098509308 -0.71157736 -0.6190102919 -0.8101660640
## 264            Dead -1.732739711 -0.01171917 -0.9714345094  0.9911466978
## 265           Alive -1.312518153  2.21664937  1.0466799279  0.0855880150
## 266           Alive -1.117483636 -1.07344208 -0.1309504223  0.5351107892
## 267           Alive -0.802242010  2.43916871 -0.0658918448  0.5326247945
## 268           Alive  1.779574174 -2.20525734 -1.2254437217 -1.4601618621
## 269            Dead -0.692885384 -0.50625416 -1.6109602188  1.2266062367
## 270           Alive -0.296827034  2.09903244 -0.5356781950  1.0212095064
## 271            Dead  2.648459041 -0.60314173 -1.1623236353 -1.1868983731
## 272           Alive -0.009329958  0.66837011 -0.6089249244 -0.0124265699
## 273           Alive  0.636626889  0.36453000 -1.0956031271 -0.4201642118
## 274           Alive -0.730329225  0.63180054 -0.2775908413  0.0076169716
## 275           Alive  0.329127497 -0.70211196 -1.1270499206 -1.3794822582
## 276           Alive -1.859016837 -0.41444458 -1.0884680056  0.0004891493
## 277           Alive  2.011187895 -1.86028031 -1.4701740451  1.9592818340
## 278            Dead  4.387657320  1.01990704 -1.0694317529  1.0313056985
## 279           Alive -1.562200265  0.50506920  0.3257902808  0.4071536855
## 280           Alive  1.140064695 -0.84165314  0.0475366423  0.1828157194
## 281           Alive -1.592089421  0.68980851  0.0241838972 -0.0763303675
## 282           Alive -0.863852065  0.20642081 -0.8983962803 -1.0667886017
## 283            Dead  1.027169030  1.16456255 -1.0404846287 -0.0396471898
## 284           Alive -0.436517354 -0.42713213  0.0134409058 -0.8973018413
## 285           Alive  0.337411799 -0.24417082 -0.6480989722 -0.0855047074
## 286            Dead  0.922063650 -0.22614793 -1.9443047687  0.7895315305
## 287           Alive  0.074518204  0.02674638 -1.0857966267  0.5553685803
## 288           Alive  0.517903752  0.07720678  0.7802091323 -0.3889323964
## 289           Alive  1.205633993  4.05992941  1.7774871852  0.5243784073
## 290            Dead  5.667322803  1.41683162  0.5192606886 -0.5242010735
## 291           Alive  0.117634314  2.05280704  1.1202906141 -0.2225732744
## 292           Alive -1.257776898  0.99085451 -0.6432249171  0.7239870280
## 293            Dead -1.442594978  0.64860803 -1.1825132672  1.3464166771
## 294           Alive  0.581815447  0.15948370  0.5111637426 -1.5852378542
## 295           Alive  3.192976367 -0.80514579  0.6934590185 -0.6145019682
## 296           Alive -1.664428065  0.44940153 -0.8138817842  0.9169350091
## 297           Alive -1.381280799 -1.04718836 -0.8104653996 -1.2130194950
## 298           Alive -0.359580844 -0.02707621 -0.2139147820  0.7519546558
## 299           Alive -1.295214100  0.90633579  0.3446284016 -0.9705650257
## 300           Alive  1.275367360 -0.46955884 -0.9321790556  1.6880185073
## 301           Alive  0.510190648 -0.47545309  0.1659852525 -1.4398287570
## 302           Alive  0.497692443  0.73632621 -0.7320867366 -0.6396358886
## 303           Alive -0.360524908  1.94049135 -0.0814679929 -1.0578009624
## 304           Alive  0.680162177  4.39853961  1.3939873156 -0.0903894719
## 305           Alive  0.651993920  1.46566547 -0.5054646735  1.4206026417
## 306            Dead  3.788964776 -1.08829199 -1.2835697130  1.5189289232
## 307           Alive  0.324102302  0.44636919 -0.0358560470 -1.7147746806
## 308           Alive  1.241627938 -0.80113200 -0.9370602561  0.5736384332
## 309           Alive -0.511968929 -1.17458566 -0.6546640582 -0.3823368294
## 310           Alive  0.718039754  0.17733890 -0.6884966946 -1.2988653722
## 311           Alive -0.310163020 -1.06311682 -0.8411613032 -0.3440185709
## 312           Alive -1.033055205  1.28803157 -0.7885399882  1.0583019502
## 313           Alive -0.764852259  0.84975776 -0.4166580478 -0.3570104900
## 314            Dead  2.840965510  1.27703956  1.2737033558 -0.0712572107
## 315           Alive -1.178758036 -0.07789715 -0.1547232721 -1.1892312531
## 316           Alive -0.802177079 -0.95036649 -0.6926590212  0.0641135168
## 317           Alive  1.938258838 -1.28408318 -0.7550485265 -0.2456973992
## 318           Alive -1.084340607  0.56509571 -0.3641566428 -0.4657496728
## 319           Alive  5.007927517  1.33213703  0.4628978606 -0.6412930066
## 320           Alive -0.352175349  0.05184295 -1.0595996323  1.1419351290
## 321           Alive -1.645893870  0.67772347  0.5678664419 -0.6516041624
## 322           Alive -0.723629619  0.28418574 -0.9155428645 -1.7398043966
## 323           Alive  2.150497872 -1.85335253 -0.9536747162 -0.9930159522
## 324           Alive  0.219479185  0.70653560  0.4625353948  0.0635989317
## 325           Alive -0.347437994  0.13601327 -0.3616040070  0.0995137840
## 326           Alive -0.234908136  0.38370796  0.3810829977  0.2955102824
## 327           Alive  0.016559745 -0.24813137  0.3418529439 -0.6289931873
## 328           Alive -1.467247701 -0.93657939 -1.0073778050 -1.3484920808
## 329           Alive  1.154836707 -1.65839860 -0.1796696786  0.5786916927
## 330           Alive  0.020892606  0.14389944  0.1408600742  0.1842691926
## 331           Alive  0.169022729  0.24173475  0.6782816134 -1.3801420819
## 332            Dead  0.596241854  0.70051500 -1.8052088015 -0.0053918173
## 333           Alive -1.658882001 -0.32657130  0.2318064743 -0.3636469103
## 334           Alive -1.130296134  0.92484749 -0.3380519552 -0.3013039197
## 335           Alive -0.114349001 -0.27920208 -0.6403335111 -0.2074405468
## 336           Alive -1.180178802  0.03183833 -0.3500656477 -1.0972084429
## 337           Alive  1.016962553 -1.84125842 -1.0359966156  0.1725787385
## 338           Alive  1.874901202 -1.13532877 -0.6093993174  1.0930613053
## 339           Alive -1.674481841  0.44986836  2.1646104925  0.9678148811
## 340           Alive  0.347838749 -0.88857174  0.8771393702 -0.0399280185
## 341           Alive -0.523787799 -0.92658682  1.5418929659  0.1325485002
## 342           Alive -1.191298001  1.23405600  1.7890495622  1.3692564275
## 343           Alive  1.808772263 -1.69685692  0.8907964331 -0.2029722962
## 344           Alive -1.770065768 -0.81617964  1.3539885104 -0.2766980579
## 345           Alive -0.206433118  0.56197089  1.8053747930  1.3814075643
## 346           Alive  0.781356058 -0.26730308  1.4981375832  0.8043655618
## 347           Alive -1.821829245 -1.41978625  1.5929954355 -0.6929508188
## 348           Alive -0.284787326 -0.98055909  2.0711730642 -0.3625595662
## 349           Alive -0.436832085  1.81979653  1.9654352950  0.0409412675
## 350           Alive -1.217940564 -0.03242505  1.5341269350  0.0689673368
## 351           Alive  1.408443279 -0.92755403  2.5527909101 -0.6932672647
## 352           Alive  0.076806137 -0.36230781  1.0569801425  0.7081503355
## 353           Alive -1.371613972 -0.73826316 -0.0390647200  0.5827617423
## 354           Alive -1.864312777 -1.17836386  1.6190160585 -0.8239266507
## 355           Alive -1.989259900 -1.78295952  1.5112558257 -0.6883823148
## 356           Alive -0.666931670  0.04442279  0.9603229118  1.9679277491
## 357           Alive -0.752021652  0.57932223  1.1919215542  0.0297044937
## 358            Dead -0.799705965 -1.07103612  0.3748144882  2.1390626788
## 359           Alive -1.601727166 -1.41026284  0.7915067164 -0.2584759327
## 360           Alive -1.657122757  0.50517962  1.7207936026  1.3778309508
## 361           Alive -0.384493964 -0.88081329  0.5179378168  0.9525680456
## 362           Alive -1.117824446  0.07013439  2.3329630062 -0.8981794794
## 363            Dead  2.156938592 -0.59054334  0.9679981313  1.4564801625
## 364            Dead -0.789754021 -2.12761614  1.4729430325  0.0219314842
## 365           Alive -1.380570918 -1.02926654  1.9974600705 -1.3875631548
## 366           Alive -1.291560292  0.38334086  1.4160677141  1.5258026469
## 367           Alive -0.935262338  0.56231264  2.1242791830  0.3720182728
## 368           Alive  2.492171120 -0.48928746  2.4676282836  1.9668068431
## 369           Alive -0.327363502 -0.84626614  2.2688783371  0.9603180211
## 370            Dead -1.468296601  0.18028669  1.6652393313  1.5773153771
## 371           Alive  0.644477407  1.35334644  2.6883609615  0.5712489712
## 372            Dead  4.369563022 -1.66481832  1.6865361527  0.4901972904
## 373           Alive -2.357052820 -1.26900605  1.5231357317  1.0301102498
## 374           Alive  0.718708019  0.22127710  1.0354060443  0.2583339391
## 375           Alive  1.391878059  0.98004221  1.7111474295 -0.7952838709
## 376           Alive  0.905097897 -0.22694710  2.1140189340  0.5476029310
## 377           Alive  3.157230391 -1.19754195  1.1484347290  1.0599855046
## 378           Alive  0.003135705 -0.90598915  1.6393299343 -1.1011824448
## 379           Alive -0.242056357 -0.73255189  1.7021620290 -0.1866470103
##              PC5          PC6          PC7
## 1   -0.332307184  0.814428206 -0.107883916
## 2    0.110810520 -0.048912344 -0.099604504
## 3   -1.007021612 -0.086507916 -0.138527863
## 4   -0.534587533 -0.822748232  0.360506834
## 5    0.527096385 -0.108812986  0.078970882
## 6   -0.430923510  0.183797925  0.433343571
## 7    0.647838054  0.008911379 -0.004657966
## 8    1.901144959  0.543125568 -0.332707934
## 9   -0.346406933 -0.752701863  0.056474342
## 10  -2.024615276 -0.441826427 -1.924448799
## 11  -0.421546565 -0.244944687  0.159851097
## 12  -0.998148360  0.206259597 -0.169273224
## 13  -0.430771477  0.163519054 -0.103667561
## 14   1.267459198  0.132474346  0.108653816
## 15  -0.309831792 -1.324055932 -0.183915616
## 16   0.235344753  0.714919089  0.304537991
## 17  -1.466753080 -0.647376538  0.365592105
## 18   0.363615703  1.097596271 -0.377715183
## 19  -1.122742523  0.334391075 -0.234827285
## 20  -0.848560671  0.808587321 -0.200036177
## 21  -0.381745196  0.322170368 -0.166529357
## 22   0.105717976  0.107803508  0.012805983
## 23  -0.572677371 -0.332323319 -0.202474142
## 24  -1.510109489  0.995998868  0.201016672
## 25  -0.807050880 -2.363493528  0.266625584
## 26  -0.466990302 -0.813907073 -0.571488560
## 27  -0.702827024 -2.160783056  0.281527887
## 28   0.009704223  0.098479393  0.336756957
## 29  -0.228150297  0.004273460 -0.381406184
## 30  -1.283048492 -0.044211599 -0.418300721
## 31   0.475434709 -0.128464996  0.054899611
## 32   0.691915088 -0.357344175  0.183909490
## 33  -0.754412318 -0.597244606  0.289672968
## 34  -0.049714847  0.259235600  0.349194654
## 35   1.283108823 -0.236888897 -0.371166651
## 36   1.416899251 -0.249251785  0.050335461
## 37   2.080438807  0.607590347 -0.462113845
## 38   0.606045480 -0.026797156  0.355817879
## 39   0.948153836  0.166045669 -0.073826942
## 40   0.304358552 -0.162738506 -0.392300116
## 41   1.462378918 -0.522507663 -0.121724380
## 42   1.234755769  0.067225848  0.209115377
## 43   0.342914980 -0.417780877 -0.474060203
## 44   0.834734733 -0.173878940 -0.457967209
## 45   1.653782254 -0.050403121 -0.134114068
## 46  -0.346353752 -0.089979747 -0.491479393
## 47   2.883679498  0.480573605 -0.072323181
## 48   1.372131721  0.228887831  0.155522234
## 49   0.900265041 -0.489991807 -0.227097997
## 50   0.515650798 -0.606582969 -0.101166456
## 51   1.854988517  0.577660866 -0.455756839
## 52  -0.039137939  0.585446120 -0.388137976
## 53  -0.406467811  0.734811073  1.561539615
## 54   0.106389455  1.381511548  0.252947237
## 55   1.220327765  0.358959045 -0.182311216
## 56   1.304773967  0.207910788  0.078632864
## 57  -1.311783436  0.607774154 -0.281869942
## 58  -1.034356670  2.443161543  0.443513680
## 59   0.092369673  0.206843192  0.253038172
## 60  -0.219974275  0.135499206  0.164773439
## 61  -0.418037102  0.648725932  0.351461678
## 62   0.736595283  0.166486526  0.246682271
## 63   0.044579623 -0.513948300 -0.286040883
## 64  -1.251280484  1.163578265  0.263125274
## 65  -0.255173442 -0.009862807  0.134046265
## 66  -0.620332594 -0.730377136  0.337181681
## 67   1.345935978 -1.487448857 -0.149925371
## 68   0.217431325  0.220853759  0.272493773
## 69  -0.390248550 -0.588054260  0.260689981
## 70  -0.266397542 -0.385273067  0.319508713
## 71  -1.764262412 -0.175254751  1.897246402
## 72   1.175874251 -1.300330063 -0.404208363
## 73   1.187096201  0.816322549 -0.225387244
## 74  -1.315635893 -0.060212427  0.165026305
## 75  -1.037240682 -1.649589162 -0.529795744
## 76  -1.564340163  0.569158827 -0.263377372
## 77   0.358667424 -0.165692949 -0.401192949
## 78   0.490508151  0.043436354  0.440699177
## 79   0.788844783  0.327782857  0.371732847
## 80   1.230687259  0.016945132  0.140928440
## 81   0.427134177 -0.877693420 -0.271276638
## 82   0.957971947  0.050656761  0.314869348
## 83   0.543187444  0.024270266 -0.489647178
## 84   1.941501550 -0.428408376  0.144447332
## 85   1.691751149  0.302353058  0.176709283
## 86   1.547734256 -0.930367776 -0.038966156
## 87   0.332021211  0.206974359  1.518547012
## 88   0.214693076  0.773220076  0.387655208
## 89   0.653638646 -0.057425863  0.311702214
## 90   0.289061393 -0.319492539 -0.104439493
## 91   0.088681106  0.464021241 -0.182053564
## 92   2.727281577  0.568469956  0.135273025
## 93   0.289629154 -0.637098352 -0.352179961
## 94   2.619577831 -0.897710356 -0.603436508
## 95   0.651509510 -0.302718373  0.134220300
## 96   1.386087535  0.796303291 -0.453234619
## 97   2.587808079  0.102248374 -0.373850042
## 98   0.697921783  0.276775028 -0.386841666
## 99  -0.394650374 -0.147547074 -2.150145655
## 100 -0.397600387  0.522935395 -0.336156710
## 101  0.716197325 -1.015284422 -0.131608533
## 102  0.172769662  0.945355253  0.288290374
## 103  2.065387989  0.240503118  0.089283023
## 104  0.047208371  0.040655927 -0.326527188
## 105 -0.041201539  0.156719385 -0.425753859
## 106 -0.195224769 -0.378077108 -0.375663969
## 107  0.919975929  0.617517671 -0.018331347
## 108 -0.453733562 -0.140360458  0.357139007
## 109 -0.561207544 -0.369058053 -0.363453154
## 110 -0.572820855  1.367651547 -0.052494633
## 111 -0.135727528 -0.245674045  0.171961839
## 112 -0.137991722 -0.288279169 -0.437854120
## 113 -0.128090086  0.654181743  0.335734007
## 114  0.019316758  0.430171258  0.242838061
## 115 -1.562982457 -0.609725681 -0.399796060
## 116  0.591477024 -0.153071461  0.293451739
## 117 -1.331526169  0.435961104  0.348338090
## 118 -1.229611547 -1.122876095  0.371334968
## 119 -0.673787799  0.128953459 -0.002950892
## 120  0.094607214  0.454338848 -0.320002000
## 121 -1.597334402 -0.393321862  0.002244332
## 122 -0.655282364  0.694427666 -1.776651924
## 123  0.248083035 -1.480360092  0.237363812
## 124 -1.061968175  0.563305776  0.061168635
## 125  0.623824012  0.789672355  0.182676841
## 126  1.220471619  0.657430786  0.151394277
## 127 -0.481456587  0.052053042 -0.260063201
## 128  0.380919478 -0.509971776  0.300299579
## 129 -0.294085119 -0.514688913  0.253498821
## 130  0.238694945 -0.230653718  0.334001823
## 131  0.325144944  0.234492897  0.070164155
## 132 -0.217308431 -0.509623760  0.211476411
## 133 -0.874193293 -0.508032972  0.218820879
## 134 -0.285329535 -0.584676128  0.432040803
## 135  0.501840322 -0.599512631  0.114578050
## 136  1.223740806  0.742555446  0.264941606
## 137 -0.355978066  0.215593238 -0.296341138
## 138 -0.744750043  0.814373445 -0.463329220
## 139 -0.100363294 -0.705236433  0.235224585
## 140 -1.581028316 -0.240819937  0.128832004
## 141 -0.361247028 -0.738265473  0.045748305
## 142 -0.054159239 -0.516065685  0.423763629
## 143  0.738930758  1.032627703  0.255695270
## 144  0.038535375  1.011640901 -0.046612704
## 145  0.108618695  1.036057364 -0.116502648
## 146 -1.731152433  0.238779557 -0.094409829
## 147 -0.203905033  0.093045275 -0.025943269
## 148  0.528132953 -0.018285774  0.063985702
## 149 -0.461933940 -0.821062597  0.316957388
## 150 -0.848242620 -0.051433159 -0.325889337
## 151 -0.148360413  0.240258258  0.157499206
## 152 -0.698788478  0.244055313 -0.484326189
## 153  0.128318661  0.321762278  0.347844280
## 154 -1.029294466 -0.688031620  0.275674116
## 155 -0.179152647  0.052870105  0.278750325
## 156 -2.192394663  0.259394959  0.994613529
## 157  0.844991207  0.384573263  0.255112420
## 158 -0.151819917 -0.647167228  0.095523521
## 159 -0.245449969 -0.447355557 -0.367626528
## 160  1.428460815 -1.037268876 -0.081314104
## 161  1.148244806  0.685349399 -0.373379228
## 162  0.631200467 -0.574402441 -0.041182433
## 163 -0.522553451 -0.812645636  0.354791023
## 164 -0.667657584  0.259528832  0.196856471
## 165 -0.148260447 -0.112837907 -0.422270866
## 166 -0.923231546  0.128000241 -0.175939627
## 167  0.053036529 -0.895512404  0.337192272
## 168 -0.985583605 -0.711019273 -0.814804273
## 169  0.450579099  0.218357219 -0.033915231
## 170 -0.798104332 -0.078144315  0.263676922
## 171 -0.865118234  0.789052948  0.069697557
## 172 -1.281949522  0.334044498  0.095799549
## 173 -0.109872739 -0.466799910  0.182242801
## 174 -0.831155436 -0.409218588  0.105315011
## 175 -1.011660986  0.475675622  0.157100174
## 176 -0.278496918  0.631970192 -0.312887516
## 177  0.590243975 -0.842796008  0.184336624
## 178  0.354044928 -0.521271064  0.253595738
## 179  0.378480572 -0.195535437 -0.489681481
## 180 -0.509222553 -0.238968439  0.339455192
## 181 -0.986316252  1.224469205  0.162311433
## 182 -0.807425073  0.896759582 -0.187133556
## 183  1.004394643 -0.369525579  0.051355060
## 184  0.392406398 -1.133798661 -0.032484936
## 185 -1.095598605 -0.525703790  0.938668397
## 186 -1.303809693  0.115704613 -0.308573611
## 187 -1.685405103 -0.330011041  0.052298230
## 188 -0.514773465  0.252831722 -0.344500770
## 189 -1.179875943  0.478267892 -0.411989559
## 190  0.106289330  0.108389410  0.270176494
## 191 -0.195203996  0.320051815 -0.452948617
## 192 -0.707539233 -0.927317654  0.050049377
## 193 -0.211477339  0.049967323  0.232020283
## 194 -0.631526388 -0.322439393 -0.332013839
## 195  0.335024707 -0.576452643  0.112196595
## 196  0.234350644 -0.426323754  0.064708147
## 197  0.012979177  0.577314293 -0.090994712
## 198 -1.308712601 -0.220002645 -0.145293651
## 199  0.202983167  1.007924154 -0.238873759
## 200 -0.917914031 -0.144916255 -0.256657796
## 201 -0.550875712  0.222523935 -0.327353336
## 202 -0.344718375  0.143637470 -0.384469784
## 203  0.256196652 -0.685873899  0.077706170
## 204  1.352914243 -0.684433914 -0.555287379
## 205 -0.342694606 -0.739601209  0.286336764
## 206 -0.036594174 -0.391145161  0.071275723
## 207 -1.104169327  1.031184262 -0.071523474
## 208 -1.594675721  0.422795216 -0.361912372
## 209 -0.578337456  0.232252275 -0.321891385
## 210 -1.218968830  0.132512399 -2.194006418
## 211 -0.374722131  0.300407101  0.236278993
## 212  1.802482148 -0.181056517 -0.655811887
## 213 -0.589252139 -2.264161275  0.013076856
## 214  0.010513237 -0.146543860  0.258375350
## 215  0.204851463 -0.914443039 -0.156858207
## 216  0.319442130  0.163052914  0.373094641
## 217  1.111404116  0.735902331  0.298434341
## 218 -1.817685120  0.858016687 -0.410620478
## 219 -0.165862050 -0.698483214  0.291328307
## 220  1.125323479 -1.702108557 -0.103054608
## 221  0.660503185 -0.570947694 -0.064210529
## 222 -0.255814803  0.103014117 -0.154551366
## 223 -0.675920517  0.032313480  0.248280548
## 224  0.075096599 -0.245512705 -0.395034205
## 225  0.066886767 -0.795643311  0.316447811
## 226 -0.435596218  0.757677018  0.355289619
## 227 -0.579002419  0.112343498 -0.370694673
## 228 -0.807029471  2.840081863 -0.472760040
## 229  0.186353531 -0.117535015  0.251369052
## 230 -1.505210536 -0.123999729 -0.103219333
## 231 -0.945826637  0.620151206 -0.398726087
## 232  0.002177941 -1.258499518  0.031686285
## 233 -0.698315265  0.508788077  0.031702502
## 234 -0.106371453 -0.730990134  0.229897436
## 235 -1.083523772 -0.131943879  0.351750927
## 236 -0.739436237  0.930178961  0.218030323
## 237  0.320606604 -1.155883577 -0.406938969
## 238 -2.013280789  0.421016873 -0.245001577
## 239  1.094774796 -0.919968833  0.339656927
## 240  0.325843132 -0.475488496  0.136247856
## 241  0.438143394  1.761754259  0.029538972
## 242 -1.112030077  1.222218060 -0.319429458
## 243 -2.030451588 -0.387563364 -0.168870331
## 244  0.241603918 -1.348003518 -0.078702906
## 245 -0.319784341 -0.096908019  0.116533237
## 246 -1.377625236  0.123274608  0.151123503
## 247 -1.217973430 -0.489960306  0.098338159
## 248  0.941303310  0.676566199 -0.339944716
## 249  0.556468021  0.072286130  0.262572292
## 250 -0.441391917 -0.203974262  0.359934672
## 251 -0.716425820 -0.962511140  0.447744836
## 252  0.139386122  0.026617023  0.293556296
## 253 -0.116189564 -0.615601226 -0.158798853
## 254  0.293324720  0.165313198  0.013008846
## 255 -1.022362433  1.432136191  1.223639292
## 256 -1.567526425  0.483977624 -0.346520349
## 257 -0.261824026 -0.153805545  0.159416002
## 258 -0.014904788 -0.327177547  0.145372443
## 259 -0.154195510  0.927279628  0.136024542
## 260 -0.279436645  0.347645497 -0.209884830
## 261  2.411185160  0.229700925 -0.104543344
## 262 -0.895962157 -0.158104523 -0.333049945
## 263 -0.107118411 -0.057284357 -0.187261115
## 264 -0.385416176 -1.002026891  0.117204649
## 265 -1.449625633  1.233710972  0.172803485
## 266 -1.625027906 -0.621049559 -0.266818669
## 267 -0.249856505  1.556396291  0.244375096
## 268  0.480018703 -0.067622566 -0.072725103
## 269  0.002189829 -0.175077307 -0.498801012
## 270  0.236744458 -0.666813685  0.155867363
## 271  1.137440016 -0.136040334 -0.327359471
## 272  0.007020687  0.778990215 -0.465309183
## 273  0.755836178  0.693723928 -0.130197667
## 274 -0.174167360 -1.468695169  0.266972231
## 275  0.788719121  0.429361577 -0.105547847
## 276  0.032889030 -0.773390730 -0.033260132
## 277 -0.863881329  0.336674762  1.064820895
## 278  0.910287718 -0.300804152  0.703841870
## 279 -1.418071805 -0.238262975  0.450690335
## 280 -1.383731574  0.395969716 -0.242043012
## 281 -0.781020214  0.109021256  0.138748544
## 282  0.713765183 -0.037963898  0.268885486
## 283  1.049317709 -0.373873694 -0.512209208
## 284 -0.722139204 -0.029714459 -0.403875221
## 285 -0.227110796  0.426625104  0.228719436
## 286  1.017821370 -0.362288537  0.223311049
## 287  0.035340926  0.384277844 -0.106878993
## 288 -1.326401252 -1.421668738  0.046595855
## 289 -0.779237256 -2.984199195  0.075859453
## 290  0.057913957  1.319916883  2.001667923
## 291 -1.394044856  2.046793198 -0.269649215
## 292 -0.267413061  0.392813424  0.303644436
## 293 -0.103965971  0.021688217  0.270137554
## 294 -0.514462082 -0.049144987 -0.046060227
## 295 -1.279398203 -1.011855498 -0.955345258
## 296 -0.409961580 -0.175912153  0.163389864
## 297  0.131190811 -0.811118093  0.416648260
## 298 -1.081305483 -0.340865035 -0.224224889
## 299 -0.587847432  0.466059600  0.157785884
## 300 -0.857351331  0.558304051 -0.192471657
## 301 -0.586650046  0.750653613  0.459663166
## 302  0.543145415  1.122352945 -0.276052847
## 303  0.492777950  1.078964668  0.210264826
## 304 -0.359689359  0.426300512  0.141513828
## 305 -0.393377040  0.810547774  0.065859782
## 306 -0.160003180 -0.181814543  1.697357273
## 307  0.185602167  0.699571022 -0.449062901
## 308 -0.380036721  0.145047367 -0.510569761
## 309 -0.528559592 -0.335948519 -0.163889426
## 310  0.666658316  0.695110312 -0.089730044
## 311 -0.239649145 -0.421019920 -0.164631917
## 312 -0.014148637 -0.328893323  0.125575320
## 313  0.163850456 -0.600269847  0.190331629
## 314 -1.299150219 -0.800239413 -0.264240505
## 315 -0.258297637 -0.079057717  0.438769076
## 316 -0.653215774 -0.386407008 -0.406110560
## 317 -0.386044302  1.041640267  0.390303651
## 318 -0.069947785 -0.189857024  0.234508553
## 319  0.335503981 -1.090183460  0.762300322
## 320 -0.354514092  0.386282802 -0.239807387
## 321 -1.130232840  0.134404520  0.127105246
## 322  1.090294733  0.366835108  0.216268360
## 323  0.090967074  0.342909111  0.372677157
## 324 -1.095438714 -0.254516438 -0.193658003
## 325 -0.602584780  0.533845103 -0.328861238
## 326 -1.313248723 -0.465612342 -0.352871158
## 327 -1.073354029 -0.163023346  0.003333250
## 328  0.464904725 -0.798713796  0.164392019
## 329 -1.773817068  0.481838526 -1.448359073
## 330 -0.953519579 -1.226111979 -0.366016068
## 331 -0.971815989  1.020308661  0.044230674
## 332  1.465700551  1.056394345 -0.394589336
## 333 -1.209182254 -1.007313550  0.374213944
## 334 -0.112208131  0.492601789  0.244276984
## 335 -0.257747260  0.411613111 -0.135788109
## 336 -0.005358715 -0.280767946  0.263720304
## 337 -0.567197423  0.160862506 -0.192753984
## 338 -1.160229327  0.791036742  0.678047807
## 339  0.135461099  0.126529280  0.120748763
## 340  1.772672225  0.262317102 -0.088849352
## 341  0.785980424  0.041119374 -0.483927739
## 342  0.892653715 -0.678266870 -0.258446039
## 343  1.489618576  1.445310485  0.036985630
## 344  1.166492368 -0.175915279  0.027902348
## 345  0.495893161  0.564004554 -0.503273137
## 346  1.134248369 -1.123890798 -0.049820336
## 347  0.865846962 -0.529962184  0.213624141
## 348  0.392274537  0.448319463 -0.109057231
## 349  1.657960929  0.164185074 -0.178027089
## 350  1.157904466  0.343302649  0.295711308
## 351  0.150225917  1.064600476 -0.399557062
## 352  1.356282603  0.402428026 -0.264910522
## 353  2.417181597 -0.039235833  0.080955691
## 354  0.990897877 -0.401278508  0.033682397
## 355  0.805384073 -0.845062983  0.190359077
## 356  0.821582895  0.916027349 -0.545821754
## 357  1.852331941  0.946629462  0.303161216
## 358  1.010092176 -0.119192699 -0.421977595
## 359  1.601877583 -0.474603729  0.232244290
## 360  0.405279647  0.620269650  0.217072532
## 361  1.560400572  0.290272477 -0.446292100
## 362  0.738754653  0.807055770  0.427223893
## 363  1.063503699  1.725250067  0.275888197
## 364  0.410727684 -0.573212533 -0.177662617
## 365  0.968366183 -0.242829260  0.310782840
## 366  0.762317564 -0.025556816  0.310309937
## 367  0.718006182 -0.369535370  0.246732337
## 368 -0.727490529  0.794924538  0.929445109
## 369 -0.407816836 -0.044906053  0.144701045
## 370  0.412661443 -0.730353345  0.202922032
## 371  0.440528158  0.105639703 -0.429239913
## 372  0.760040778 -0.245135971  0.186120856
## 373  0.074632682 -0.823120736  0.174853047
## 374  1.891779073  1.126518713 -0.084801083
## 375  2.265775349 -0.200011773 -0.549385252
## 376  0.603860387 -1.229143214  0.135743929
## 377  1.186962665 -0.299503313  0.743333133
## 378  1.359035590  0.410392839 -0.361555114
## 379  0.800865246  0.837670932 -0.196874004
# Means of scores for all the PC's classified by Survival status
tabmeansPC <- aggregate(sparrtyp_pca[,2:6],by=list(Survivor=Cancer$Survivor),mean)
tabmeansPC
##   Survivor       PC1         PC2        PC3         PC4        PC5
## 1    Alive -0.191643 -0.04773213  0.1087994 -0.08377152 -0.1049705
## 2     Dead  1.039420  0.25888613 -0.5900986  0.45435399  0.5693316
## Inference
## PC1, the mean value for the Alive group is negative (-0.191643), while for the Dead group, it is positive (1.039420), indicating that PC1 has a strong influence on separating the two groups. Similarly, for PC2 and PC5, the mean values for the Dead group are higher than those for the Alive group, indicating that these components also contribute to the separation of the two groups.
## For PC3 and PC4, the mean values are positive for the Alive group and negative for the Dead group. This suggests that these components are less important in distinguishing between the two groups of cancer patients.

tabmeansPC <- tabmeansPC[rev(order(tabmeansPC$Survivor)),]
tabmeansPC
##   Survivor       PC1         PC2        PC3         PC4        PC5
## 2     Dead  1.039420  0.25888613 -0.5900986  0.45435399  0.5693316
## 1    Alive -0.191643 -0.04773213  0.1087994 -0.08377152 -0.1049705
## From the tabmeansPC we can infer that the patients who died have higher average values of PC1 to PC5 compared to those who survived.

tabfmeans <- t(tabmeansPC[,-1])
tabfmeans
##              2           1
## PC1  1.0394196 -0.19164299
## PC2  0.2588861 -0.04773213
## PC3 -0.5900986  0.10879943
## PC4  0.4543540 -0.08377152
## PC5  0.5693316 -0.10497052
colnames(tabfmeans) <- t(as.vector(tabmeansPC[1]$Survivor))
tabfmeans
##           Dead       Alive
## PC1  1.0394196 -0.19164299
## PC2  0.2588861 -0.04773213
## PC3 -0.5900986  0.10879943
## PC4  0.4543540 -0.08377152
## PC5  0.5693316 -0.10497052
# Standard deviations of scores for all the PC's classified by Survival status
tabsdsPC <- aggregate(sparrtyp_pca[,2:6],by=list(Survivor=Cancer$Survivor),sd)
tabfsds <- t(tabsdsPC[,-1])
colnames(tabfsds) <- t(as.vector(tabsdsPC[1]$Survivor))
tabfsds
##         Alive      Dead
## PC1 1.3045077 1.9921081
## PC2 1.0622596 1.1781697
## PC3 0.9845002 1.0805810
## PC4 0.9561011 0.9236866
## PC5 0.9104233 0.8906488
t.test(PC1~Cancer$Survivor,data=sparrtyp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC1 by Cancer$Survivor
## t = -4.5695, df = 67.457, p-value = 2.14e-05
## alternative hypothesis: true difference in means between group Alive and group Dead is not equal to 0
## 95 percent confidence interval:
##  -1.7687358 -0.6933893
## sample estimates:
## mean in group Alive  mean in group Dead 
##           -0.191643            1.039420
## The t-test is used to determine whether there is a significant difference between the mean PC1 scores of the "Alive" and "Dead" groups.
## The output shows that the t-statistic is -4.5695 and the p-value is 2.14e-05, which is much less than 0.05, the commonly used significance level. Therefore, we reject the null hypothesis and conclude that there is a significant difference between the mean PC1 scores of the "Alive" and "Dead" groups.

t.test(PC2~Cancer$Survivor,data=sparrtyp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC2 by Cancer$Survivor
## t = -1.8642, df = 76.377, p-value = 0.06614
## alternative hypothesis: true difference in means between group Alive and group Dead is not equal to 0
## 95 percent confidence interval:
##  -0.63417884  0.02094233
## sample estimates:
## mean in group Alive  mean in group Dead 
##         -0.04773213          0.25888613
## For PC2, the p-value of the t-test is greater than 0.05, indicating that there is no strong evidence to suggest that the mean values of PC2 are different between the two groups.

t.test(PC3~Cancer$Survivor,data=sparrtyp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC3 by Cancer$Survivor
## t = 4.6266, df = 76.785, p-value = 1.482e-05
## alternative hypothesis: true difference in means between group Alive and group Dead is not equal to 0
## 95 percent confidence interval:
##  0.3980823 0.9997138
## sample estimates:
## mean in group Alive  mean in group Dead 
##           0.1087994          -0.5900986
## The p-values for the t-tests of PC1, PC2, and PC3 between the two groups (Alive and Dead) are 2.14e-05, 0.06614, and 1.482e-05, respectively. These p-values indicate that there is strong evidence to reject the null hypothesis of no difference in the mean values of the principal components between the two groups for PC1 and PC3. 
## However, for PC2, the p-value is relatively high (0.06614), which suggests that there is no strong evidence to reject the null hypothesis of no difference in the mean values of PC2 between the two groups.
t.test(PC4~Cancer$Survivor,data=sparrtyp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC4 by Cancer$Survivor
## t = -4.0892, df = 82.592, p-value = 9.998e-05
## alternative hypothesis: true difference in means between group Alive and group Dead is not equal to 0
## 95 percent confidence interval:
##  -0.7998846 -0.2763664
## sample estimates:
## mean in group Alive  mean in group Dead 
##         -0.08377152          0.45435399
## Based on the t-tests, we can see that there are significant differences in the means of PC1, PC3, and PC4 between the Alive and Dead groups, as evidenced by their low p-values (p < 0.05). However, there is no significant difference in the means of PC2 between the two groups (p > 0.05).

t.test(PC5~Cancer$Survivor,data=sparrtyp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC5 by Cancer$Survivor
## t = -5.325, df = 81.947, p-value = 8.655e-07
## alternative hypothesis: true difference in means between group Alive and group Dead is not equal to 0
## 95 percent confidence interval:
##  -0.9262125 -0.4223918
## sample estimates:
## mean in group Alive  mean in group Dead 
##          -0.1049705           0.5693316
## F ratio tests
var.test(PC1~Cancer$Survivor,data=sparrtyp_pca)
## 
##  F test to compare two variances
## 
## data:  PC1 by Cancer$Survivor
## F = 0.42881, num df = 319, denom df = 58, p-value = 3.503e-06
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.2799208 0.6214510
## sample estimates:
## ratio of variances 
##          0.4288125
var.test(PC2~Cancer$Survivor,data=sparrtyp_pca)
## 
##  F test to compare two variances
## 
## data:  PC2 by Cancer$Survivor
## F = 0.81292, num df = 319, denom df = 58, p-value = 0.2734
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.5306564 1.1781079
## sample estimates:
## ratio of variances 
##          0.8129159
var.test(PC3~Cancer$Survivor,data=sparrtyp_pca)
## 
##  F test to compare two variances
## 
## data:  PC3 by Cancer$Survivor
## F = 0.83007, num df = 319, denom df = 58, p-value = 0.3235
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.5418571 1.2029746
## sample estimates:
## ratio of variances 
##          0.8300744
var.test(PC4~Cancer$Survivor,data=sparrtyp_pca)
## 
##  F test to compare two variances
## 
## data:  PC4 by Cancer$Survivor
## F = 1.0714, num df = 319, denom df = 58, p-value = 0.7705
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.6994008 1.5527366
## sample estimates:
## ratio of variances 
##           1.071417
var.test(PC5~Cancer$Survivor,data=sparrtyp_pca)
## 
##  F test to compare two variances
## 
## data:  PC5 by Cancer$Survivor
## F = 1.0449, num df = 319, denom df = 58, p-value = 0.8655
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.6820898 1.5143045
## sample estimates:
## ratio of variances 
##           1.044898
# Levene's tests (one-sided)
library(car)
## Loading required package: carData
## 
## Attaching package: 'car'
## 
## The following object is masked from 'package:purrr':
## 
##     some
## 
## The following object is masked from 'package:dplyr':
## 
##     recode
(LTPC1 <- leveneTest(PC1~Cancer$Survivor,data=sparrtyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   1  13.637 0.0002545 ***
##       377                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC1_1sided <- LTPC1[[3]][1]/2)
## [1] 0.0001272506
(LTPC2 <- leveneTest(PC2~Cancer$Survivor,data=sparrtyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   1  2.0564 0.1524
##       377
(p_PC2_1sided=LTPC2[[3]][1]/2)
## [1] 0.0761985
(LTPC3 <- leveneTest(PC3~Cancer$Survivor,data=sparrtyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   1  0.1773 0.6739
##       377
(p_PC3_1sided <- LTPC3[[3]][1]/2)
## [1] 0.3369607
(LTPC4 <- leveneTest(PC4~Cancer$Survivor,data=sparrtyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   1  0.1316  0.717
##       377
(p_PC4_1sided <- LTPC4[[3]][1]/2)
## [1] 0.358511
(LTPC5 <- leveneTest(PC5~Cancer$Survivor,data=sparrtyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   1  0.0035  0.953
##       377
(p_PC5_1sided <- LTPC5[[3]][1]/2)
## [1] 0.4765143
# Plotting the scores for the first and second components
plot(eigen_Cancer, xlab = "Component number", ylab = "Component variance", type = "l", main = "Scree Diagram")

plot(log(eigen_Cancer), xlab = "Component number",ylab = "log(Component variance)", type="l",main = "Log(eigenvalue) diagram")

print(summary(Cancer_pca))
## Importance of components:
##                           PC1    PC2    PC3    PC4    PC5     PC6     PC7
## Standard deviation     1.4983 1.0852 1.0303 0.9698 0.9387 0.71218 0.43271
## Proportion of Variance 0.3207 0.1682 0.1516 0.1344 0.1259 0.07246 0.02675
## Cumulative Proportion  0.3207 0.4889 0.6406 0.7749 0.9008 0.97325 1.00000
diag(cov(Cancer_pca$x))
##       PC1       PC2       PC3       PC4       PC5       PC6       PC7 
## 2.2447716 1.1776466 1.0614934 0.9405242 0.8811341 0.5071959 0.1872342
xlim <- range(Cancer_pca$x[,1])
Cancer_pca$x[,1]
##   [1] -1.441559363  0.466697152  1.724644704 -1.727412749  0.084534880
##   [6] -0.987174108 -1.289312885  0.457476281  5.013544810  1.966110970
##  [11] -1.709742154  1.323214712 -0.047344848 -0.023379894  1.042993427
##  [16] -0.954171084 -0.510183493  0.248390384 -0.386424810 -0.212235416
##  [21]  0.001291199  0.547237523 -0.581794885  1.484574719  0.730385134
##  [26]  1.384044724  2.503197607 -1.094732396 -0.040233637 -0.913495245
##  [31]  0.044817272 -1.310023914 -1.750326793 -0.860691537  1.293140200
##  [36] -1.575412171  0.505620687 -1.445729993 -0.240634131 -0.335231355
##  [41]  2.392046521 -1.496209472 -1.238156754 -0.122858339 -1.614959830
##  [46]  0.653344872 -0.903132282 -1.570956435  0.407142180 -2.095133885
##  [51]  0.145196356  0.438754344  2.005777230  1.526981600 -1.762004433
##  [56] -1.584099552 -0.496130040 -0.310631363 -1.133478035 -1.203472671
##  [61] -0.899762531 -1.006446958 -0.437812701  1.712300783 -1.263885916
##  [66] -1.604219653  4.488026052 -0.665172931 -1.668377900 -1.130422629
##  [71]  3.316812797  2.172380940  0.572326326 -1.827615023  0.720276568
##  [76]  0.849193077 -0.640547040 -0.095120639 -0.045215749 -1.769164273
##  [81]  0.718379560 -1.678008963 -0.895860760 -1.627068924 -1.331489281
##  [86]  0.909892498  2.680823986  1.353531002 -1.678967186 -2.304099591
##  [91]  0.741204117 -0.809147683 -0.790428226  1.549314451 -1.647991336
##  [96] -0.268121798 -0.103534223 -0.776307350  1.103113756 -0.409442426
## [101]  4.633190126 -0.740349810  0.704221402 -0.385204834 -0.068793640
## [106] -0.692576410  0.345220609 -1.364096376 -0.387521866  0.491580932
## [111] -1.087373932  1.210180885  1.869006469  0.492734252  0.889433533
## [116] -0.849321798  1.382626614 -0.876114257  0.129510618  0.006142764
## [121] -0.669636518  1.757579745  1.875711497  0.312604564 -0.681074580
## [126] -0.863182056 -0.118572831 -1.423953866 -1.441335172 -0.856545337
## [131] -1.307398005  0.585398503 -1.786207788 -1.427017695  0.756062138
## [136]  0.145449916 -0.274324587 -0.438129117  1.064299809  2.098096298
## [141] -1.849943605 -0.732556857 -0.608595125  0.505611656  0.247551976
## [146] -0.602802743 -1.272341157  2.651497970 -1.824221268 -0.352147008
## [151] -1.129437762 -0.549974224 -1.104925141 -1.260493668 -1.263788087
## [156]  2.182293451 -0.839030427 -1.567211240 -0.656681669  1.746317858
## [161]  0.576848393 -1.591129974 -1.734769097 -1.257058960  0.171012852
## [166]  0.763873736 -0.648233872  4.075761272  0.108096807 -1.498040609
## [171]  0.047885996  1.337596168 -1.358485537 -1.872027381 -1.311243234
## [176]  1.309706033 -0.190859319 -1.150520519  1.562083350  0.457663612
## [181] -1.138195339 -0.007740653 -1.442466409  1.401099127  3.044609211
## [186] -0.608848019  0.869481448 -0.300778748  0.636747830 -1.117892469
## [191] -0.433517740 -2.074508151 -0.943857160 -0.671437346  3.146400023
## [196] -1.646968799  0.194381857  1.355794604  0.342080981 -0.390007297
## [201] -0.278709707 -0.042662340 -1.773111892  1.250439359 -1.763032603
## [206] -1.734908122 -0.040455138 -0.686284826 -0.444359734  0.691490501
## [211]  2.007551495  2.980951104 -0.051043670 -1.433696923  0.663189426
## [216]  2.031410016  0.789603453  0.673484381 -1.540903396  4.811125983
## [221]  2.960210184  0.548555090 -1.203818787 -0.095903547 -1.447284264
## [226] -0.721456172  2.040310983  1.855207556 -1.362709085 -0.288896751
## [231] -0.418601999 -1.163850583  0.411132602 -1.693135796 -1.469262447
## [236] -1.241804213  3.689808324  0.637785394  6.741912903 -1.238593026
## [241]  0.823175506  0.046147404 -0.926653518  1.642861658  0.577872627
## [246] -1.754825326 -2.038325012  0.534102452 -0.778602587 -1.358620602
## [251]  0.552972231  0.160512695 -0.255760964  2.380048532  2.562080786
## [256] -0.556325503 -1.361977024 -1.604168388  0.453544197 -0.245088734
## [261] -0.586494355 -0.595783004 -0.098509308 -1.732739711 -1.312518153
## [266] -1.117483636 -0.802242010  1.779574174 -0.692885384 -0.296827034
## [271]  2.648459041 -0.009329958  0.636626889 -0.730329225  0.329127497
## [276] -1.859016837  2.011187895  4.387657320 -1.562200265  1.140064695
## [281] -1.592089421 -0.863852065  1.027169030 -0.436517354  0.337411799
## [286]  0.922063650  0.074518204  0.517903752  1.205633993  5.667322803
## [291]  0.117634314 -1.257776898 -1.442594978  0.581815447  3.192976367
## [296] -1.664428065 -1.381280799 -0.359580844 -1.295214100  1.275367360
## [301]  0.510190648  0.497692443 -0.360524908  0.680162177  0.651993920
## [306]  3.788964776  0.324102302  1.241627938 -0.511968929  0.718039754
## [311] -0.310163020 -1.033055205 -0.764852259  2.840965510 -1.178758036
## [316] -0.802177079  1.938258838 -1.084340607  5.007927517 -0.352175349
## [321] -1.645893870 -0.723629619  2.150497872  0.219479185 -0.347437994
## [326] -0.234908136  0.016559745 -1.467247701  1.154836707  0.020892606
## [331]  0.169022729  0.596241854 -1.658882001 -1.130296134 -0.114349001
## [336] -1.180178802  1.016962553  1.874901202 -1.674481841  0.347838749
## [341] -0.523787799 -1.191298001  1.808772263 -1.770065768 -0.206433118
## [346]  0.781356058 -1.821829245 -0.284787326 -0.436832085 -1.217940564
## [351]  1.408443279  0.076806137 -1.371613972 -1.864312777 -1.989259900
## [356] -0.666931670 -0.752021652 -0.799705965 -1.601727166 -1.657122757
## [361] -0.384493964 -1.117824446  2.156938592 -0.789754021 -1.380570918
## [366] -1.291560292 -0.935262338  2.492171120 -0.327363502 -1.468296601
## [371]  0.644477407  4.369563022 -2.357052820  0.718708019  1.391878059
## [376]  0.905097897  3.157230391  0.003135705 -0.242056357
Cancer_pca$x
##                 PC1         PC2           PC3           PC4          PC5
##   [1,] -1.441559363  1.84595445 -0.3691842456  0.8313546497 -0.332307184
##   [2,]  0.466697152  0.06803649 -0.6236808487 -0.3679040103  0.110810520
##   [3,]  1.724644704 -0.46933933 -0.1593826887  0.5351088884 -1.007021612
##   [4,] -1.727412749 -0.67153366 -0.6471303735 -0.0657071859 -0.534587533
##   [5,]  0.084534880 -1.24252757 -1.5702796993 -0.3040439925  0.527096385
##   [6,] -0.987174108  0.58301426  0.1669091720 -0.9999683133 -0.430923510
##   [7,] -1.289312885  0.33343114 -1.1225709379 -0.4660831193  0.647838054
##   [8,]  0.457476281 -0.43703336 -2.3348237400 -0.5798103154  1.901144959
##   [9,]  5.013544810 -0.35127563  0.3138865965 -0.6789485742 -0.346406933
##  [10,]  1.966110970  0.57900951  0.8436785098  1.1971488330 -2.024615276
##  [11,] -1.709742154  0.39272616 -0.8797546127  1.0395229446 -0.421546565
##  [12,]  1.323214712 -1.40692828  0.0010448762 -0.8532983622 -0.998148360
##  [13,] -0.047344848  0.20982069 -0.8615166802  1.1288786920 -0.430771477
##  [14,] -0.023379894  1.83512622 -0.8543600804 -0.5919635549  1.267459198
##  [15,]  1.042993427  1.19479846 -0.1106365956  0.7578922926 -0.309831792
##  [16,] -0.954171084  1.25373181 -0.8631921253  0.4922727293  0.235344753
##  [17,] -0.510183493 -1.74284660 -0.1083044907 -0.2184460954 -1.466753080
##  [18,]  0.248390384  0.43156365 -0.4623851738 -1.2333483190  0.363615703
##  [19,] -0.386424810 -0.37494859  0.5477775527 -1.3442739171 -1.122742523
##  [20,] -0.212235416  0.44848661 -0.0814638947  0.1978257208 -0.848560671
##  [21,]  0.001291199 -0.22401731 -0.1753398416 -0.9042251252 -0.381745196
##  [22,]  0.547237523  0.35323566 -0.8945832960  0.4857434118  0.105717976
##  [23,] -0.581794885 -1.07033107 -0.7283097731 -0.0629010628 -0.572677371
##  [24,]  1.484574719 -1.12275223  0.4930197218 -0.8534326311 -1.510109489
##  [25,]  0.730385134  3.01009366  1.5328340955 -0.0845516282 -0.807050880
##  [26,]  1.384044724  2.86730858  0.7935319092  0.4879719811 -0.466990302
##  [27,]  2.503197607  1.86942247  1.6035708576 -1.0898911376 -0.702827024
##  [28,] -1.094732396  0.13919430 -0.2430526831 -1.3348711724  0.009704223
##  [29,] -0.040233637  0.24894946 -0.5823916977  0.1870202613 -0.228150297
##  [30,] -0.913495245 -0.27255918 -0.2249052502  0.7136559763 -1.283048492
##  [31,]  0.044817272 -1.24749459 -1.5147400984 -0.3403352312  0.475434709
##  [32,] -1.310023914 -0.18810081 -1.5041631045 -0.0748728835  0.691915088
##  [33,] -1.750326793 -0.31441971 -0.3126381565 -0.1365620557 -0.754412318
##  [34,] -0.860691537  1.17774354 -0.4731321013  0.2383866081 -0.049714847
##  [35,]  1.293140200  1.12837700 -1.0955034983 -0.3513923420  1.283108823
##  [36,] -1.575412171 -0.65517742  1.1178980897 -0.0145585733  1.416899251
##  [37,]  0.505620687  0.48204717  0.6768751198  0.9826148200  2.080438807
##  [38,] -1.445729993 -0.53420180  2.0397881463 -0.4191403509  0.606045480
##  [39,] -0.240634131 -1.38008841  1.2981310791  0.0234566336  0.948153836
##  [40,] -0.335231355 -0.71567154  2.2622815166 -0.2598837684  0.304358552
##  [41,]  2.392046521 -0.75381886  0.6808155988  1.7849935943  1.462378918
##  [42,] -1.496209472 -0.05147919  0.8362058172  1.4463882147  1.234755769
##  [43,] -1.238156754 -1.73396163  1.0838915624  1.1966166369  0.342914980
##  [44,] -0.122858339 -0.41520397  1.7259286489  0.2467343049  0.834734733
##  [45,] -1.614959830 -0.21262796  0.8270352673  0.5084458503  1.653782254
##  [46,]  0.653344872 -1.45282335  1.6923961454  1.7730389364 -0.346353752
##  [47,] -0.903132282  0.00288121  0.2891894480 -0.3828977838  2.883679498
##  [48,] -1.570956435 -0.13307164  0.7378711359  1.2691205943  1.372131721
##  [49,]  0.407142180 -0.18484286  1.8224576827  0.3406571927  0.900265041
##  [50,] -2.095133885 -0.24603762  1.3075254314  1.5865972660  0.515650798
##  [51,]  0.145196356 -0.72051716  1.2885099274 -1.1072761596  1.854988517
##  [52,]  0.438754344 -1.67207421  0.9831353778  2.3512915236 -0.039137939
##  [53,]  2.005777230 -2.95342227  1.2688959631  1.7356814675 -0.406467811
##  [54,]  1.526981600 -1.02119752  1.4223445513  1.8001650835  0.106389455
##  [55,] -1.762004433  0.13389155  1.3060891880  0.4365138287  1.220327765
##  [56,] -1.584099552 -0.27233552  1.1461680461  0.3643457178  1.304773967
##  [57,] -0.496130040  0.33490544  0.2711418287  0.1648088615 -1.311783436
##  [58,] -0.310631363  3.07311289  1.8743230894 -1.7983452746 -1.034356670
##  [59,] -1.133478035  0.41599332 -0.4379284603 -0.8528069490  0.092369673
##  [60,] -1.203472671  0.78226143 -0.1914939617 -0.4844823758 -0.219974275
##  [61,] -0.899762531  1.31926126  0.1811318594 -0.4938217806 -0.418037102
##  [62,] -1.006446958  0.35539993 -1.2221294160 -0.3469217710  0.736595283
##  [63,] -0.437812701 -1.58636590 -0.8897438306 -1.2595916576  0.044579623
##  [64,]  1.712300783 -0.45593265 -0.1013381728  0.5911078860 -1.251280484
##  [65,] -1.263885916  1.17224839 -0.6291534095  0.9206949813 -0.255173442
##  [66,] -1.604219653 -0.82712464  0.0494208809 -1.5797529143 -0.620332594
##  [67,]  4.488026052  1.14176192 -0.1231038156 -1.5112898673  1.345935978
##  [68,] -0.665172931  0.68451038  0.1453995807 -2.0258292592  0.217431325
##  [69,] -1.668377900 -0.33091730 -0.6606673180 -0.0526400595 -0.390248550
##  [70,] -1.130422629  0.23695569 -0.1769384999 -0.7612337767 -0.266397542
##  [71,]  3.316812797 -1.81535426  0.5502180418 -0.2694003925 -1.764262412
##  [72,]  2.172380940  2.85911092 -0.9844345887  1.6403461146  1.175874251
##  [73,]  0.572326326 -0.34757898 -1.0234096521 -2.0869344002  1.187096201
##  [74,] -1.827615023  0.62057292  0.3016558087  0.2426806849 -1.315635893
##  [75,]  0.720276568  1.70219107  0.6872975038  0.8005007414 -1.037240682
##  [76,]  0.849193077 -1.14260361  0.1217975270 -0.0272015985 -1.564340163
##  [77,] -0.640547040 -0.61272303  1.3854969929  1.5959470836  0.358667424
##  [78,] -0.095120639 -2.25942107  1.7743414136 -0.8570595769  0.490508151
##  [79,] -0.045215749 -1.67214619  1.1930256589  0.3311124134  0.788844783
##  [80,] -1.769164273 -0.22777378  0.5215512977  1.9330657865  1.230687259
##  [81,]  0.718379560  0.42702578  2.7049430509  0.0009902972  0.427134177
##  [82,] -1.678008963 -0.30727716  0.8345249461  1.7090923528  0.957971947
##  [83,] -0.895860760 -0.84819969  1.0351097886  1.6955225348  0.543187444
##  [84,] -1.627068924 -1.17405222  0.1883777552  0.6241466387  1.941501550
##  [85,] -1.331489281 -0.34160016  0.9121167916  0.1344506975  1.691751149
##  [86,]  0.909892498 -0.53731582  1.4060161653 -0.0311065615  1.547734256
##  [87,]  2.680823986 -2.87516871  1.2736995009  0.6959415006  0.332021211
##  [88,]  1.353531002 -2.37316783  1.3254482077  0.7127875562  0.214693076
##  [89,] -1.678967186 -0.70552936  1.6695940259  0.1038284595  0.653638646
##  [90,] -2.304099591 -0.48981820  1.6210427235  0.9780934643  0.289061393
##  [91,]  0.741204117 -2.34543537  1.4452706433  0.5998522096  0.088681106
##  [92,] -0.809147683 -0.48805441  0.7203787577 -1.4686194537  2.727281577
##  [93,] -0.790428226 -1.28394744  1.3498973595  1.2856985141  0.289629154
##  [94,]  1.549314451  1.05942412  1.1109895492  0.1457696503  2.619577831
##  [95,] -1.647991336 -0.27927996  1.6891990873  0.5048525410  0.651509510
##  [96,] -0.268121798 -0.13194343  0.7385162603  1.3684964706  1.386087535
##  [97,] -0.103534223 -1.33945241 -0.5191543874  1.0167737783  2.587808079
##  [98,] -0.776307350 -0.99454099  1.0504553950  1.2109563269  0.697921783
##  [99,]  1.103113756 -1.77799849 -1.0931648334 -0.0122323381 -0.394650374
## [100,] -0.409442426  0.35492707 -1.0502000077  1.4204609639 -0.397600387
## [101,]  4.633190126  2.16526818  0.6239105977 -1.1366907435  0.716197325
## [102,] -0.740349810  1.21149156 -0.0348952140 -1.2669488699  0.172769662
## [103,]  0.704221402 -1.11279489 -2.7553374907 -0.4028612238  2.065387989
## [104,] -0.385204834 -0.52764189 -1.2886177272  0.4419425766  0.047208371
## [105,] -0.068793640  0.07508422 -0.6067830446 -0.3162015548 -0.041201539
## [106,] -0.692576410 -0.91636560 -1.3471231484  0.7054513599 -0.195224769
## [107,]  0.345220609 -0.15476507 -1.9375149484  0.6213467649  0.919975929
## [108,] -1.364096376  0.64909093 -0.7204212843  1.0498159217 -0.453733562
## [109,] -0.387521866 -1.16290394  0.1995560232 -2.1751452860 -0.561207544
## [110,]  0.491580932  1.59726077 -0.0288299149  0.6365139827 -0.572820855
## [111,] -1.087373932  0.96622658 -0.4850478973  0.2957151405 -0.135727528
## [112,]  1.210180885 -2.10091879 -0.7122063654 -1.4443151802 -0.137991722
## [113,]  1.869006469  1.83583553  0.7046224722 -1.0701872221 -0.128090086
## [114,]  0.492734252 -0.45633393 -0.5614007104 -0.8951702764  0.019316758
## [115,]  0.889433533 -1.50731469  0.2004002058 -0.2364464439 -1.562982457
## [116,] -0.849321798  0.50645649 -1.0584322308 -0.1780669707  0.591477024
## [117,]  1.382626614 -1.86070361 -0.1224339395 -0.3673855944 -1.331526169
## [118,] -0.876114257  1.31244321  0.5402724456  0.6865577157 -1.229611547
## [119,]  0.129510618 -0.29073195  0.1371234823 -1.0140234437 -0.673787799
## [120,]  0.006142764  0.12672993 -0.8224846986 -0.0976817279  0.094607214
## [121,] -0.669636518 -0.67017693 -0.0910644210  0.8278709329 -1.597334402
## [122,]  1.757579745 -1.15217572 -0.1806146788 -1.0023054945 -0.655282364
## [123,]  1.875711497  0.92049908 -0.1305383937 -0.2267912179  0.248083035
## [124,]  0.312604564  0.73821191  0.3983729256  0.0063600881 -1.061968175
## [125,] -0.681074580  1.46363098 -0.7243706847 -0.3192569625  0.623824012
## [126,] -0.863182056  1.24685123 -1.9912585523  1.1497711812  1.220471619
## [127,] -0.118572831 -0.70053670  0.2417380654 -2.0356708316 -0.481456587
## [128,] -1.423953866 -0.28566927 -1.5423434161  0.5267774639  0.380919478
## [129,] -1.441335172 -0.03524627 -0.5051970790 -0.2755060729 -0.294085119
## [130,] -0.856545337  0.21574546 -0.3501704930 -1.3208020069  0.238694945
## [131,] -1.307398005  0.79423090 -1.0835136941  0.4150931199  0.325144944
## [132,]  0.585398503 -0.41679342 -0.4499848326 -0.4042504411 -0.217308431
## [133,] -1.786207788 -0.17673804 -0.0665424655 -0.3670738391 -0.874193293
## [134,] -1.427017695 -0.63688709 -0.4649731902 -0.8892591027 -0.285329535
## [135,]  0.756062138 -0.13112369 -1.3636990615  0.5752861401  0.501840322
## [136,]  0.145449916  1.69976295 -0.3153802001 -1.9246355296  1.223740806
## [137,] -0.274324587 -0.57433529 -0.2583518619 -1.1336704462 -0.355978066
## [138,] -0.438129117  0.74050108 -0.3404267839  0.7633673055 -0.744750043
## [139,]  1.064299809  0.61136855 -0.6550235320  0.9211144934 -0.100363294
## [140,]  2.098096298 -0.42706015  0.8620866598 -0.4563567888 -1.581028316
## [141,] -1.849943605 -0.47094945 -0.5180573283 -0.5701157634 -0.361247028
## [142,] -0.732556857 -0.13070679  0.3510392562 -2.5238550573 -0.054159239
## [143,] -0.608595125  1.35155467 -0.7057542462 -0.7165766057  0.738930758
## [144,]  0.505611656  1.09999711 -0.8457725436  0.9361832967  0.038535375
## [145,]  0.247551976  0.46673882 -0.7913160371  0.0399880240  0.108618695
## [146,] -0.602802743 -0.23260921  0.5437161698 -0.0788003168 -1.731152433
## [147,] -1.272341157  0.63788399  0.2396679916 -1.6177473606 -0.203905033
## [148,]  2.651497970 -0.83742214 -0.8602918415 -0.9187276925  0.528132953
## [149,] -1.824221268 -0.45358497 -1.0788845841  0.9216453730 -0.461933940
## [150,] -0.352147008 -0.02439510 -0.1582340020  0.1140579142 -0.848242620
## [151,] -1.129437762  0.24550127  0.4252415970 -2.4757263934 -0.148360413
## [152,] -0.549974224  0.36383145 -0.6269521199  1.0856493132 -0.698788478
## [153,] -1.104925141  0.73145555 -0.9068622646  0.3853904201  0.128318661
## [154,] -1.260493668  0.67356911  0.3950426508 -0.1537212632 -1.029294466
## [155,] -1.263788087  0.89343258 -0.8613170835  1.0342322348 -0.179152647
## [156,]  2.182293451 -0.70621431  0.3489551723  1.5351765574 -2.192394663
## [157,] -0.839030427  0.51161725 -1.0551051340 -0.7935641661  0.844991207
## [158,] -1.567211240 -0.76592187 -0.0382695651 -2.2426462201 -0.151819917
## [159,] -0.656681669 -1.17053344 -1.0085651375 -0.1509452878 -0.245449969
## [160,]  1.746317858  1.20029090 -1.6249506696  0.9407644883  1.428460815
## [161,]  0.576848393  1.03248254 -1.8769456788  1.1403757019  1.148244806
## [162,] -1.591129974 -0.30100995 -1.4737482868 -0.1586928611  0.631200467
## [163,] -1.734769097 -0.63230165 -0.6993991424  0.0578306174 -0.522553451
## [164,] -1.257058960  0.98743371  0.2695795040 -0.5173988569 -0.667657584
## [165,]  0.171012852  0.73662045 -0.6335336460  0.6662455703 -0.148260447
## [166,]  0.763873736 -1.48595671 -1.3893183822  1.8933152957 -0.923231546
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## [359,] -1.601727166 -1.41026284  0.7915067164 -0.2584759327  1.601877583
## [360,] -1.657122757  0.50517962  1.7207936026  1.3778309508  0.405279647
## [361,] -0.384493964 -0.88081329  0.5179378168  0.9525680456  1.560400572
## [362,] -1.117824446  0.07013439  2.3329630062 -0.8981794794  0.738754653
## [363,]  2.156938592 -0.59054334  0.9679981313  1.4564801625  1.063503699
## [364,] -0.789754021 -2.12761614  1.4729430325  0.0219314842  0.410727684
## [365,] -1.380570918 -1.02926654  1.9974600705 -1.3875631548  0.968366183
## [366,] -1.291560292  0.38334086  1.4160677141  1.5258026469  0.762317564
## [367,] -0.935262338  0.56231264  2.1242791830  0.3720182728  0.718006182
## [368,]  2.492171120 -0.48928746  2.4676282836  1.9668068431 -0.727490529
## [369,] -0.327363502 -0.84626614  2.2688783371  0.9603180211 -0.407816836
## [370,] -1.468296601  0.18028669  1.6652393313  1.5773153771  0.412661443
## [371,]  0.644477407  1.35334644  2.6883609615  0.5712489712  0.440528158
## [372,]  4.369563022 -1.66481832  1.6865361527  0.4901972904  0.760040778
## [373,] -2.357052820 -1.26900605  1.5231357317  1.0301102498  0.074632682
## [374,]  0.718708019  0.22127710  1.0354060443  0.2583339391  1.891779073
## [375,]  1.391878059  0.98004221  1.7111474295 -0.7952838709  2.265775349
## [376,]  0.905097897 -0.22694710  2.1140189340  0.5476029310  0.603860387
## [377,]  3.157230391 -1.19754195  1.1484347290  1.0599855046  1.186962665
## [378,]  0.003135705 -0.90598915  1.6393299343 -1.1011824448  1.359035590
## [379,] -0.242056357 -0.73255189  1.7021620290 -0.1866470103  0.800865246
##                 PC6          PC7
##   [1,]  0.814428206 -0.107883916
##   [2,] -0.048912344 -0.099604504
##   [3,] -0.086507916 -0.138527863
##   [4,] -0.822748232  0.360506834
##   [5,] -0.108812986  0.078970882
##   [6,]  0.183797925  0.433343571
##   [7,]  0.008911379 -0.004657966
##   [8,]  0.543125568 -0.332707934
##   [9,] -0.752701863  0.056474342
##  [10,] -0.441826427 -1.924448799
##  [11,] -0.244944687  0.159851097
##  [12,]  0.206259597 -0.169273224
##  [13,]  0.163519054 -0.103667561
##  [14,]  0.132474346  0.108653816
##  [15,] -1.324055932 -0.183915616
##  [16,]  0.714919089  0.304537991
##  [17,] -0.647376538  0.365592105
##  [18,]  1.097596271 -0.377715183
##  [19,]  0.334391075 -0.234827285
##  [20,]  0.808587321 -0.200036177
##  [21,]  0.322170368 -0.166529357
##  [22,]  0.107803508  0.012805983
##  [23,] -0.332323319 -0.202474142
##  [24,]  0.995998868  0.201016672
##  [25,] -2.363493528  0.266625584
##  [26,] -0.813907073 -0.571488560
##  [27,] -2.160783056  0.281527887
##  [28,]  0.098479393  0.336756957
##  [29,]  0.004273460 -0.381406184
##  [30,] -0.044211599 -0.418300721
##  [31,] -0.128464996  0.054899611
##  [32,] -0.357344175  0.183909490
##  [33,] -0.597244606  0.289672968
##  [34,]  0.259235600  0.349194654
##  [35,] -0.236888897 -0.371166651
##  [36,] -0.249251785  0.050335461
##  [37,]  0.607590347 -0.462113845
##  [38,] -0.026797156  0.355817879
##  [39,]  0.166045669 -0.073826942
##  [40,] -0.162738506 -0.392300116
##  [41,] -0.522507663 -0.121724380
##  [42,]  0.067225848  0.209115377
##  [43,] -0.417780877 -0.474060203
##  [44,] -0.173878940 -0.457967209
##  [45,] -0.050403121 -0.134114068
##  [46,] -0.089979747 -0.491479393
##  [47,]  0.480573605 -0.072323181
##  [48,]  0.228887831  0.155522234
##  [49,] -0.489991807 -0.227097997
##  [50,] -0.606582969 -0.101166456
##  [51,]  0.577660866 -0.455756839
##  [52,]  0.585446120 -0.388137976
##  [53,]  0.734811073  1.561539615
##  [54,]  1.381511548  0.252947237
##  [55,]  0.358959045 -0.182311216
##  [56,]  0.207910788  0.078632864
##  [57,]  0.607774154 -0.281869942
##  [58,]  2.443161543  0.443513680
##  [59,]  0.206843192  0.253038172
##  [60,]  0.135499206  0.164773439
##  [61,]  0.648725932  0.351461678
##  [62,]  0.166486526  0.246682271
##  [63,] -0.513948300 -0.286040883
##  [64,]  1.163578265  0.263125274
##  [65,] -0.009862807  0.134046265
##  [66,] -0.730377136  0.337181681
##  [67,] -1.487448857 -0.149925371
##  [68,]  0.220853759  0.272493773
##  [69,] -0.588054260  0.260689981
##  [70,] -0.385273067  0.319508713
##  [71,] -0.175254751  1.897246402
##  [72,] -1.300330063 -0.404208363
##  [73,]  0.816322549 -0.225387244
##  [74,] -0.060212427  0.165026305
##  [75,] -1.649589162 -0.529795744
##  [76,]  0.569158827 -0.263377372
##  [77,] -0.165692949 -0.401192949
##  [78,]  0.043436354  0.440699177
##  [79,]  0.327782857  0.371732847
##  [80,]  0.016945132  0.140928440
##  [81,] -0.877693420 -0.271276638
##  [82,]  0.050656761  0.314869348
##  [83,]  0.024270266 -0.489647178
##  [84,] -0.428408376  0.144447332
##  [85,]  0.302353058  0.176709283
##  [86,] -0.930367776 -0.038966156
##  [87,]  0.206974359  1.518547012
##  [88,]  0.773220076  0.387655208
##  [89,] -0.057425863  0.311702214
##  [90,] -0.319492539 -0.104439493
##  [91,]  0.464021241 -0.182053564
##  [92,]  0.568469956  0.135273025
##  [93,] -0.637098352 -0.352179961
##  [94,] -0.897710356 -0.603436508
##  [95,] -0.302718373  0.134220300
##  [96,]  0.796303291 -0.453234619
##  [97,]  0.102248374 -0.373850042
##  [98,]  0.276775028 -0.386841666
##  [99,] -0.147547074 -2.150145655
## [100,]  0.522935395 -0.336156710
## [101,] -1.015284422 -0.131608533
## [102,]  0.945355253  0.288290374
## [103,]  0.240503118  0.089283023
## [104,]  0.040655927 -0.326527188
## [105,]  0.156719385 -0.425753859
## [106,] -0.378077108 -0.375663969
## [107,]  0.617517671 -0.018331347
## [108,] -0.140360458  0.357139007
## [109,] -0.369058053 -0.363453154
## [110,]  1.367651547 -0.052494633
## [111,] -0.245674045  0.171961839
## [112,] -0.288279169 -0.437854120
## [113,]  0.654181743  0.335734007
## [114,]  0.430171258  0.242838061
## [115,] -0.609725681 -0.399796060
## [116,] -0.153071461  0.293451739
## [117,]  0.435961104  0.348338090
## [118,] -1.122876095  0.371334968
## [119,]  0.128953459 -0.002950892
## [120,]  0.454338848 -0.320002000
## [121,] -0.393321862  0.002244332
## [122,]  0.694427666 -1.776651924
## [123,] -1.480360092  0.237363812
## [124,]  0.563305776  0.061168635
## [125,]  0.789672355  0.182676841
## [126,]  0.657430786  0.151394277
## [127,]  0.052053042 -0.260063201
## [128,] -0.509971776  0.300299579
## [129,] -0.514688913  0.253498821
## [130,] -0.230653718  0.334001823
## [131,]  0.234492897  0.070164155
## [132,] -0.509623760  0.211476411
## [133,] -0.508032972  0.218820879
## [134,] -0.584676128  0.432040803
## [135,] -0.599512631  0.114578050
## [136,]  0.742555446  0.264941606
## [137,]  0.215593238 -0.296341138
## [138,]  0.814373445 -0.463329220
## [139,] -0.705236433  0.235224585
## [140,] -0.240819937  0.128832004
## [141,] -0.738265473  0.045748305
## [142,] -0.516065685  0.423763629
## [143,]  1.032627703  0.255695270
## [144,]  1.011640901 -0.046612704
## [145,]  1.036057364 -0.116502648
## [146,]  0.238779557 -0.094409829
## [147,]  0.093045275 -0.025943269
## [148,] -0.018285774  0.063985702
## [149,] -0.821062597  0.316957388
## [150,] -0.051433159 -0.325889337
## [151,]  0.240258258  0.157499206
## [152,]  0.244055313 -0.484326189
## [153,]  0.321762278  0.347844280
## [154,] -0.688031620  0.275674116
## [155,]  0.052870105  0.278750325
## [156,]  0.259394959  0.994613529
## [157,]  0.384573263  0.255112420
## [158,] -0.647167228  0.095523521
## [159,] -0.447355557 -0.367626528
## [160,] -1.037268876 -0.081314104
## [161,]  0.685349399 -0.373379228
## [162,] -0.574402441 -0.041182433
## [163,] -0.812645636  0.354791023
## [164,]  0.259528832  0.196856471
## [165,] -0.112837907 -0.422270866
## [166,]  0.128000241 -0.175939627
## [167,] -0.895512404  0.337192272
## [168,] -0.711019273 -0.814804273
## [169,]  0.218357219 -0.033915231
## [170,] -0.078144315  0.263676922
## [171,]  0.789052948  0.069697557
## [172,]  0.334044498  0.095799549
## [173,] -0.466799910  0.182242801
## [174,] -0.409218588  0.105315011
## [175,]  0.475675622  0.157100174
## [176,]  0.631970192 -0.312887516
## [177,] -0.842796008  0.184336624
## [178,] -0.521271064  0.253595738
## [179,] -0.195535437 -0.489681481
## [180,] -0.238968439  0.339455192
## [181,]  1.224469205  0.162311433
## [182,]  0.896759582 -0.187133556
## [183,] -0.369525579  0.051355060
## [184,] -1.133798661 -0.032484936
## [185,] -0.525703790  0.938668397
## [186,]  0.115704613 -0.308573611
## [187,] -0.330011041  0.052298230
## [188,]  0.252831722 -0.344500770
## [189,]  0.478267892 -0.411989559
## [190,]  0.108389410  0.270176494
## [191,]  0.320051815 -0.452948617
## [192,] -0.927317654  0.050049377
## [193,]  0.049967323  0.232020283
## [194,] -0.322439393 -0.332013839
## [195,] -0.576452643  0.112196595
## [196,] -0.426323754  0.064708147
## [197,]  0.577314293 -0.090994712
## [198,] -0.220002645 -0.145293651
## [199,]  1.007924154 -0.238873759
## [200,] -0.144916255 -0.256657796
## [201,]  0.222523935 -0.327353336
## [202,]  0.143637470 -0.384469784
## [203,] -0.685873899  0.077706170
## [204,] -0.684433914 -0.555287379
## [205,] -0.739601209  0.286336764
## [206,] -0.391145161  0.071275723
## [207,]  1.031184262 -0.071523474
## [208,]  0.422795216 -0.361912372
## [209,]  0.232252275 -0.321891385
## [210,]  0.132512399 -2.194006418
## [211,]  0.300407101  0.236278993
## [212,] -0.181056517 -0.655811887
## [213,] -2.264161275  0.013076856
## [214,] -0.146543860  0.258375350
## [215,] -0.914443039 -0.156858207
## [216,]  0.163052914  0.373094641
## [217,]  0.735902331  0.298434341
## [218,]  0.858016687 -0.410620478
## [219,] -0.698483214  0.291328307
## [220,] -1.702108557 -0.103054608
## [221,] -0.570947694 -0.064210529
## [222,]  0.103014117 -0.154551366
## [223,]  0.032313480  0.248280548
## [224,] -0.245512705 -0.395034205
## [225,] -0.795643311  0.316447811
## [226,]  0.757677018  0.355289619
## [227,]  0.112343498 -0.370694673
## [228,]  2.840081863 -0.472760040
## [229,] -0.117535015  0.251369052
## [230,] -0.123999729 -0.103219333
## [231,]  0.620151206 -0.398726087
## [232,] -1.258499518  0.031686285
## [233,]  0.508788077  0.031702502
## [234,] -0.730990134  0.229897436
## [235,] -0.131943879  0.351750927
## [236,]  0.930178961  0.218030323
## [237,] -1.155883577 -0.406938969
## [238,]  0.421016873 -0.245001577
## [239,] -0.919968833  0.339656927
## [240,] -0.475488496  0.136247856
## [241,]  1.761754259  0.029538972
## [242,]  1.222218060 -0.319429458
## [243,] -0.387563364 -0.168870331
## [244,] -1.348003518 -0.078702906
## [245,] -0.096908019  0.116533237
## [246,]  0.123274608  0.151123503
## [247,] -0.489960306  0.098338159
## [248,]  0.676566199 -0.339944716
## [249,]  0.072286130  0.262572292
## [250,] -0.203974262  0.359934672
## [251,] -0.962511140  0.447744836
## [252,]  0.026617023  0.293556296
## [253,] -0.615601226 -0.158798853
## [254,]  0.165313198  0.013008846
## [255,]  1.432136191  1.223639292
## [256,]  0.483977624 -0.346520349
## [257,] -0.153805545  0.159416002
## [258,] -0.327177547  0.145372443
## [259,]  0.927279628  0.136024542
## [260,]  0.347645497 -0.209884830
## [261,]  0.229700925 -0.104543344
## [262,] -0.158104523 -0.333049945
## [263,] -0.057284357 -0.187261115
## [264,] -1.002026891  0.117204649
## [265,]  1.233710972  0.172803485
## [266,] -0.621049559 -0.266818669
## [267,]  1.556396291  0.244375096
## [268,] -0.067622566 -0.072725103
## [269,] -0.175077307 -0.498801012
## [270,] -0.666813685  0.155867363
## [271,] -0.136040334 -0.327359471
## [272,]  0.778990215 -0.465309183
## [273,]  0.693723928 -0.130197667
## [274,] -1.468695169  0.266972231
## [275,]  0.429361577 -0.105547847
## [276,] -0.773390730 -0.033260132
## [277,]  0.336674762  1.064820895
## [278,] -0.300804152  0.703841870
## [279,] -0.238262975  0.450690335
## [280,]  0.395969716 -0.242043012
## [281,]  0.109021256  0.138748544
## [282,] -0.037963898  0.268885486
## [283,] -0.373873694 -0.512209208
## [284,] -0.029714459 -0.403875221
## [285,]  0.426625104  0.228719436
## [286,] -0.362288537  0.223311049
## [287,]  0.384277844 -0.106878993
## [288,] -1.421668738  0.046595855
## [289,] -2.984199195  0.075859453
## [290,]  1.319916883  2.001667923
## [291,]  2.046793198 -0.269649215
## [292,]  0.392813424  0.303644436
## [293,]  0.021688217  0.270137554
## [294,] -0.049144987 -0.046060227
## [295,] -1.011855498 -0.955345258
## [296,] -0.175912153  0.163389864
## [297,] -0.811118093  0.416648260
## [298,] -0.340865035 -0.224224889
## [299,]  0.466059600  0.157785884
## [300,]  0.558304051 -0.192471657
## [301,]  0.750653613  0.459663166
## [302,]  1.122352945 -0.276052847
## [303,]  1.078964668  0.210264826
## [304,]  0.426300512  0.141513828
## [305,]  0.810547774  0.065859782
## [306,] -0.181814543  1.697357273
## [307,]  0.699571022 -0.449062901
## [308,]  0.145047367 -0.510569761
## [309,] -0.335948519 -0.163889426
## [310,]  0.695110312 -0.089730044
## [311,] -0.421019920 -0.164631917
## [312,] -0.328893323  0.125575320
## [313,] -0.600269847  0.190331629
## [314,] -0.800239413 -0.264240505
## [315,] -0.079057717  0.438769076
## [316,] -0.386407008 -0.406110560
## [317,]  1.041640267  0.390303651
## [318,] -0.189857024  0.234508553
## [319,] -1.090183460  0.762300322
## [320,]  0.386282802 -0.239807387
## [321,]  0.134404520  0.127105246
## [322,]  0.366835108  0.216268360
## [323,]  0.342909111  0.372677157
## [324,] -0.254516438 -0.193658003
## [325,]  0.533845103 -0.328861238
## [326,] -0.465612342 -0.352871158
## [327,] -0.163023346  0.003333250
## [328,] -0.798713796  0.164392019
## [329,]  0.481838526 -1.448359073
## [330,] -1.226111979 -0.366016068
## [331,]  1.020308661  0.044230674
## [332,]  1.056394345 -0.394589336
## [333,] -1.007313550  0.374213944
## [334,]  0.492601789  0.244276984
## [335,]  0.411613111 -0.135788109
## [336,] -0.280767946  0.263720304
## [337,]  0.160862506 -0.192753984
## [338,]  0.791036742  0.678047807
## [339,]  0.126529280  0.120748763
## [340,]  0.262317102 -0.088849352
## [341,]  0.041119374 -0.483927739
## [342,] -0.678266870 -0.258446039
## [343,]  1.445310485  0.036985630
## [344,] -0.175915279  0.027902348
## [345,]  0.564004554 -0.503273137
## [346,] -1.123890798 -0.049820336
## [347,] -0.529962184  0.213624141
## [348,]  0.448319463 -0.109057231
## [349,]  0.164185074 -0.178027089
## [350,]  0.343302649  0.295711308
## [351,]  1.064600476 -0.399557062
## [352,]  0.402428026 -0.264910522
## [353,] -0.039235833  0.080955691
## [354,] -0.401278508  0.033682397
## [355,] -0.845062983  0.190359077
## [356,]  0.916027349 -0.545821754
## [357,]  0.946629462  0.303161216
## [358,] -0.119192699 -0.421977595
## [359,] -0.474603729  0.232244290
## [360,]  0.620269650  0.217072532
## [361,]  0.290272477 -0.446292100
## [362,]  0.807055770  0.427223893
## [363,]  1.725250067  0.275888197
## [364,] -0.573212533 -0.177662617
## [365,] -0.242829260  0.310782840
## [366,] -0.025556816  0.310309937
## [367,] -0.369535370  0.246732337
## [368,]  0.794924538  0.929445109
## [369,] -0.044906053  0.144701045
## [370,] -0.730353345  0.202922032
## [371,]  0.105639703 -0.429239913
## [372,] -0.245135971  0.186120856
## [373,] -0.823120736  0.174853047
## [374,]  1.126518713 -0.084801083
## [375,] -0.200011773 -0.549385252
## [376,] -1.229143214  0.135743929
## [377,] -0.299503313  0.743333133
## [378,]  0.410392839 -0.361555114
## [379,]  0.837670932 -0.196874004
Cancer_pca$rotation[,1]
##                    Age                  Stage             Tumor Size 
##            -0.21487519             0.56017028             0.57902017 
## Regional Node Examined  Reginol Node Positive        Survival Months 
##             0.23910247             0.45785153            -0.18008353 
##                    Sex 
##            -0.07446786
Cancer_pca$rotation
##                                PC1        PC2          PC3         PC4
## Age                    -0.21487519  0.2043145  0.027261393  0.85973142
## Stage                   0.56017028 -0.3373169  0.011318788  0.11956737
## Tumor Size              0.57902017 -0.2934857 -0.007289973  0.15966422
## Regional Node Examined  0.23910247  0.6987477  0.329462796 -0.11137816
## Reginol Node Positive   0.45785153  0.3946611  0.191113542  0.03278061
## Survival Months        -0.18008353 -0.1898301  0.618720758 -0.33346116
## Sex                    -0.07446786 -0.2798176  0.686432853  0.31047844
##                                PC5         PC6         PC7
## Age                    -0.41336263 -0.03629602 -0.00410619
## Stage                  -0.21766761  0.18269976 -0.69082826
## Tumor Size             -0.13361696  0.13694401  0.71864375
## Regional Node Examined -0.03947383  0.57624593  0.00365182
## Reginol Node Positive   0.10540722 -0.76394463 -0.04789123
## Survival Months        -0.63971799 -0.15748760  0.05900235
## Sex                     0.58479969  0.07795267 -0.02241484
Cancer_pca$x
##                 PC1         PC2           PC3           PC4          PC5
##   [1,] -1.441559363  1.84595445 -0.3691842456  0.8313546497 -0.332307184
##   [2,]  0.466697152  0.06803649 -0.6236808487 -0.3679040103  0.110810520
##   [3,]  1.724644704 -0.46933933 -0.1593826887  0.5351088884 -1.007021612
##   [4,] -1.727412749 -0.67153366 -0.6471303735 -0.0657071859 -0.534587533
##   [5,]  0.084534880 -1.24252757 -1.5702796993 -0.3040439925  0.527096385
##   [6,] -0.987174108  0.58301426  0.1669091720 -0.9999683133 -0.430923510
##   [7,] -1.289312885  0.33343114 -1.1225709379 -0.4660831193  0.647838054
##   [8,]  0.457476281 -0.43703336 -2.3348237400 -0.5798103154  1.901144959
##   [9,]  5.013544810 -0.35127563  0.3138865965 -0.6789485742 -0.346406933
##  [10,]  1.966110970  0.57900951  0.8436785098  1.1971488330 -2.024615276
##  [11,] -1.709742154  0.39272616 -0.8797546127  1.0395229446 -0.421546565
##  [12,]  1.323214712 -1.40692828  0.0010448762 -0.8532983622 -0.998148360
##  [13,] -0.047344848  0.20982069 -0.8615166802  1.1288786920 -0.430771477
##  [14,] -0.023379894  1.83512622 -0.8543600804 -0.5919635549  1.267459198
##  [15,]  1.042993427  1.19479846 -0.1106365956  0.7578922926 -0.309831792
##  [16,] -0.954171084  1.25373181 -0.8631921253  0.4922727293  0.235344753
##  [17,] -0.510183493 -1.74284660 -0.1083044907 -0.2184460954 -1.466753080
##  [18,]  0.248390384  0.43156365 -0.4623851738 -1.2333483190  0.363615703
##  [19,] -0.386424810 -0.37494859  0.5477775527 -1.3442739171 -1.122742523
##  [20,] -0.212235416  0.44848661 -0.0814638947  0.1978257208 -0.848560671
##  [21,]  0.001291199 -0.22401731 -0.1753398416 -0.9042251252 -0.381745196
##  [22,]  0.547237523  0.35323566 -0.8945832960  0.4857434118  0.105717976
##  [23,] -0.581794885 -1.07033107 -0.7283097731 -0.0629010628 -0.572677371
##  [24,]  1.484574719 -1.12275223  0.4930197218 -0.8534326311 -1.510109489
##  [25,]  0.730385134  3.01009366  1.5328340955 -0.0845516282 -0.807050880
##  [26,]  1.384044724  2.86730858  0.7935319092  0.4879719811 -0.466990302
##  [27,]  2.503197607  1.86942247  1.6035708576 -1.0898911376 -0.702827024
##  [28,] -1.094732396  0.13919430 -0.2430526831 -1.3348711724  0.009704223
##  [29,] -0.040233637  0.24894946 -0.5823916977  0.1870202613 -0.228150297
##  [30,] -0.913495245 -0.27255918 -0.2249052502  0.7136559763 -1.283048492
##  [31,]  0.044817272 -1.24749459 -1.5147400984 -0.3403352312  0.475434709
##  [32,] -1.310023914 -0.18810081 -1.5041631045 -0.0748728835  0.691915088
##  [33,] -1.750326793 -0.31441971 -0.3126381565 -0.1365620557 -0.754412318
##  [34,] -0.860691537  1.17774354 -0.4731321013  0.2383866081 -0.049714847
##  [35,]  1.293140200  1.12837700 -1.0955034983 -0.3513923420  1.283108823
##  [36,] -1.575412171 -0.65517742  1.1178980897 -0.0145585733  1.416899251
##  [37,]  0.505620687  0.48204717  0.6768751198  0.9826148200  2.080438807
##  [38,] -1.445729993 -0.53420180  2.0397881463 -0.4191403509  0.606045480
##  [39,] -0.240634131 -1.38008841  1.2981310791  0.0234566336  0.948153836
##  [40,] -0.335231355 -0.71567154  2.2622815166 -0.2598837684  0.304358552
##  [41,]  2.392046521 -0.75381886  0.6808155988  1.7849935943  1.462378918
##  [42,] -1.496209472 -0.05147919  0.8362058172  1.4463882147  1.234755769
##  [43,] -1.238156754 -1.73396163  1.0838915624  1.1966166369  0.342914980
##  [44,] -0.122858339 -0.41520397  1.7259286489  0.2467343049  0.834734733
##  [45,] -1.614959830 -0.21262796  0.8270352673  0.5084458503  1.653782254
##  [46,]  0.653344872 -1.45282335  1.6923961454  1.7730389364 -0.346353752
##  [47,] -0.903132282  0.00288121  0.2891894480 -0.3828977838  2.883679498
##  [48,] -1.570956435 -0.13307164  0.7378711359  1.2691205943  1.372131721
##  [49,]  0.407142180 -0.18484286  1.8224576827  0.3406571927  0.900265041
##  [50,] -2.095133885 -0.24603762  1.3075254314  1.5865972660  0.515650798
##  [51,]  0.145196356 -0.72051716  1.2885099274 -1.1072761596  1.854988517
##  [52,]  0.438754344 -1.67207421  0.9831353778  2.3512915236 -0.039137939
##  [53,]  2.005777230 -2.95342227  1.2688959631  1.7356814675 -0.406467811
##  [54,]  1.526981600 -1.02119752  1.4223445513  1.8001650835  0.106389455
##  [55,] -1.762004433  0.13389155  1.3060891880  0.4365138287  1.220327765
##  [56,] -1.584099552 -0.27233552  1.1461680461  0.3643457178  1.304773967
##  [57,] -0.496130040  0.33490544  0.2711418287  0.1648088615 -1.311783436
##  [58,] -0.310631363  3.07311289  1.8743230894 -1.7983452746 -1.034356670
##  [59,] -1.133478035  0.41599332 -0.4379284603 -0.8528069490  0.092369673
##  [60,] -1.203472671  0.78226143 -0.1914939617 -0.4844823758 -0.219974275
##  [61,] -0.899762531  1.31926126  0.1811318594 -0.4938217806 -0.418037102
##  [62,] -1.006446958  0.35539993 -1.2221294160 -0.3469217710  0.736595283
##  [63,] -0.437812701 -1.58636590 -0.8897438306 -1.2595916576  0.044579623
##  [64,]  1.712300783 -0.45593265 -0.1013381728  0.5911078860 -1.251280484
##  [65,] -1.263885916  1.17224839 -0.6291534095  0.9206949813 -0.255173442
##  [66,] -1.604219653 -0.82712464  0.0494208809 -1.5797529143 -0.620332594
##  [67,]  4.488026052  1.14176192 -0.1231038156 -1.5112898673  1.345935978
##  [68,] -0.665172931  0.68451038  0.1453995807 -2.0258292592  0.217431325
##  [69,] -1.668377900 -0.33091730 -0.6606673180 -0.0526400595 -0.390248550
##  [70,] -1.130422629  0.23695569 -0.1769384999 -0.7612337767 -0.266397542
##  [71,]  3.316812797 -1.81535426  0.5502180418 -0.2694003925 -1.764262412
##  [72,]  2.172380940  2.85911092 -0.9844345887  1.6403461146  1.175874251
##  [73,]  0.572326326 -0.34757898 -1.0234096521 -2.0869344002  1.187096201
##  [74,] -1.827615023  0.62057292  0.3016558087  0.2426806849 -1.315635893
##  [75,]  0.720276568  1.70219107  0.6872975038  0.8005007414 -1.037240682
##  [76,]  0.849193077 -1.14260361  0.1217975270 -0.0272015985 -1.564340163
##  [77,] -0.640547040 -0.61272303  1.3854969929  1.5959470836  0.358667424
##  [78,] -0.095120639 -2.25942107  1.7743414136 -0.8570595769  0.490508151
##  [79,] -0.045215749 -1.67214619  1.1930256589  0.3311124134  0.788844783
##  [80,] -1.769164273 -0.22777378  0.5215512977  1.9330657865  1.230687259
##  [81,]  0.718379560  0.42702578  2.7049430509  0.0009902972  0.427134177
##  [82,] -1.678008963 -0.30727716  0.8345249461  1.7090923528  0.957971947
##  [83,] -0.895860760 -0.84819969  1.0351097886  1.6955225348  0.543187444
##  [84,] -1.627068924 -1.17405222  0.1883777552  0.6241466387  1.941501550
##  [85,] -1.331489281 -0.34160016  0.9121167916  0.1344506975  1.691751149
##  [86,]  0.909892498 -0.53731582  1.4060161653 -0.0311065615  1.547734256
##  [87,]  2.680823986 -2.87516871  1.2736995009  0.6959415006  0.332021211
##  [88,]  1.353531002 -2.37316783  1.3254482077  0.7127875562  0.214693076
##  [89,] -1.678967186 -0.70552936  1.6695940259  0.1038284595  0.653638646
##  [90,] -2.304099591 -0.48981820  1.6210427235  0.9780934643  0.289061393
##  [91,]  0.741204117 -2.34543537  1.4452706433  0.5998522096  0.088681106
##  [92,] -0.809147683 -0.48805441  0.7203787577 -1.4686194537  2.727281577
##  [93,] -0.790428226 -1.28394744  1.3498973595  1.2856985141  0.289629154
##  [94,]  1.549314451  1.05942412  1.1109895492  0.1457696503  2.619577831
##  [95,] -1.647991336 -0.27927996  1.6891990873  0.5048525410  0.651509510
##  [96,] -0.268121798 -0.13194343  0.7385162603  1.3684964706  1.386087535
##  [97,] -0.103534223 -1.33945241 -0.5191543874  1.0167737783  2.587808079
##  [98,] -0.776307350 -0.99454099  1.0504553950  1.2109563269  0.697921783
##  [99,]  1.103113756 -1.77799849 -1.0931648334 -0.0122323381 -0.394650374
## [100,] -0.409442426  0.35492707 -1.0502000077  1.4204609639 -0.397600387
## [101,]  4.633190126  2.16526818  0.6239105977 -1.1366907435  0.716197325
## [102,] -0.740349810  1.21149156 -0.0348952140 -1.2669488699  0.172769662
## [103,]  0.704221402 -1.11279489 -2.7553374907 -0.4028612238  2.065387989
## [104,] -0.385204834 -0.52764189 -1.2886177272  0.4419425766  0.047208371
## [105,] -0.068793640  0.07508422 -0.6067830446 -0.3162015548 -0.041201539
## [106,] -0.692576410 -0.91636560 -1.3471231484  0.7054513599 -0.195224769
## [107,]  0.345220609 -0.15476507 -1.9375149484  0.6213467649  0.919975929
## [108,] -1.364096376  0.64909093 -0.7204212843  1.0498159217 -0.453733562
## [109,] -0.387521866 -1.16290394  0.1995560232 -2.1751452860 -0.561207544
## [110,]  0.491580932  1.59726077 -0.0288299149  0.6365139827 -0.572820855
## [111,] -1.087373932  0.96622658 -0.4850478973  0.2957151405 -0.135727528
## [112,]  1.210180885 -2.10091879 -0.7122063654 -1.4443151802 -0.137991722
## [113,]  1.869006469  1.83583553  0.7046224722 -1.0701872221 -0.128090086
## [114,]  0.492734252 -0.45633393 -0.5614007104 -0.8951702764  0.019316758
## [115,]  0.889433533 -1.50731469  0.2004002058 -0.2364464439 -1.562982457
## [116,] -0.849321798  0.50645649 -1.0584322308 -0.1780669707  0.591477024
## [117,]  1.382626614 -1.86070361 -0.1224339395 -0.3673855944 -1.331526169
## [118,] -0.876114257  1.31244321  0.5402724456  0.6865577157 -1.229611547
## [119,]  0.129510618 -0.29073195  0.1371234823 -1.0140234437 -0.673787799
## [120,]  0.006142764  0.12672993 -0.8224846986 -0.0976817279  0.094607214
## [121,] -0.669636518 -0.67017693 -0.0910644210  0.8278709329 -1.597334402
## [122,]  1.757579745 -1.15217572 -0.1806146788 -1.0023054945 -0.655282364
## [123,]  1.875711497  0.92049908 -0.1305383937 -0.2267912179  0.248083035
## [124,]  0.312604564  0.73821191  0.3983729256  0.0063600881 -1.061968175
## [125,] -0.681074580  1.46363098 -0.7243706847 -0.3192569625  0.623824012
## [126,] -0.863182056  1.24685123 -1.9912585523  1.1497711812  1.220471619
## [127,] -0.118572831 -0.70053670  0.2417380654 -2.0356708316 -0.481456587
## [128,] -1.423953866 -0.28566927 -1.5423434161  0.5267774639  0.380919478
## [129,] -1.441335172 -0.03524627 -0.5051970790 -0.2755060729 -0.294085119
## [130,] -0.856545337  0.21574546 -0.3501704930 -1.3208020069  0.238694945
## [131,] -1.307398005  0.79423090 -1.0835136941  0.4150931199  0.325144944
## [132,]  0.585398503 -0.41679342 -0.4499848326 -0.4042504411 -0.217308431
## [133,] -1.786207788 -0.17673804 -0.0665424655 -0.3670738391 -0.874193293
## [134,] -1.427017695 -0.63688709 -0.4649731902 -0.8892591027 -0.285329535
## [135,]  0.756062138 -0.13112369 -1.3636990615  0.5752861401  0.501840322
## [136,]  0.145449916  1.69976295 -0.3153802001 -1.9246355296  1.223740806
## [137,] -0.274324587 -0.57433529 -0.2583518619 -1.1336704462 -0.355978066
## [138,] -0.438129117  0.74050108 -0.3404267839  0.7633673055 -0.744750043
## [139,]  1.064299809  0.61136855 -0.6550235320  0.9211144934 -0.100363294
## [140,]  2.098096298 -0.42706015  0.8620866598 -0.4563567888 -1.581028316
## [141,] -1.849943605 -0.47094945 -0.5180573283 -0.5701157634 -0.361247028
## [142,] -0.732556857 -0.13070679  0.3510392562 -2.5238550573 -0.054159239
## [143,] -0.608595125  1.35155467 -0.7057542462 -0.7165766057  0.738930758
## [144,]  0.505611656  1.09999711 -0.8457725436  0.9361832967  0.038535375
## [145,]  0.247551976  0.46673882 -0.7913160371  0.0399880240  0.108618695
## [146,] -0.602802743 -0.23260921  0.5437161698 -0.0788003168 -1.731152433
## [147,] -1.272341157  0.63788399  0.2396679916 -1.6177473606 -0.203905033
## [148,]  2.651497970 -0.83742214 -0.8602918415 -0.9187276925  0.528132953
## [149,] -1.824221268 -0.45358497 -1.0788845841  0.9216453730 -0.461933940
## [150,] -0.352147008 -0.02439510 -0.1582340020  0.1140579142 -0.848242620
## [151,] -1.129437762  0.24550127  0.4252415970 -2.4757263934 -0.148360413
## [152,] -0.549974224  0.36383145 -0.6269521199  1.0856493132 -0.698788478
## [153,] -1.104925141  0.73145555 -0.9068622646  0.3853904201  0.128318661
## [154,] -1.260493668  0.67356911  0.3950426508 -0.1537212632 -1.029294466
## [155,] -1.263788087  0.89343258 -0.8613170835  1.0342322348 -0.179152647
## [156,]  2.182293451 -0.70621431  0.3489551723  1.5351765574 -2.192394663
## [157,] -0.839030427  0.51161725 -1.0551051340 -0.7935641661  0.844991207
## [158,] -1.567211240 -0.76592187 -0.0382695651 -2.2426462201 -0.151819917
## [159,] -0.656681669 -1.17053344 -1.0085651375 -0.1509452878 -0.245449969
## [160,]  1.746317858  1.20029090 -1.6249506696  0.9407644883  1.428460815
## [161,]  0.576848393  1.03248254 -1.8769456788  1.1403757019  1.148244806
## [162,] -1.591129974 -0.30100995 -1.4737482868 -0.1586928611  0.631200467
## [163,] -1.734769097 -0.63230165 -0.6993991424  0.0578306174 -0.522553451
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## [356,] -0.666931670  0.04442279  0.9603229118  1.9679277491  0.821582895
## [357,] -0.752021652  0.57932223  1.1919215542  0.0297044937  1.852331941
## [358,] -0.799705965 -1.07103612  0.3748144882  2.1390626788  1.010092176
## [359,] -1.601727166 -1.41026284  0.7915067164 -0.2584759327  1.601877583
## [360,] -1.657122757  0.50517962  1.7207936026  1.3778309508  0.405279647
## [361,] -0.384493964 -0.88081329  0.5179378168  0.9525680456  1.560400572
## [362,] -1.117824446  0.07013439  2.3329630062 -0.8981794794  0.738754653
## [363,]  2.156938592 -0.59054334  0.9679981313  1.4564801625  1.063503699
## [364,] -0.789754021 -2.12761614  1.4729430325  0.0219314842  0.410727684
## [365,] -1.380570918 -1.02926654  1.9974600705 -1.3875631548  0.968366183
## [366,] -1.291560292  0.38334086  1.4160677141  1.5258026469  0.762317564
## [367,] -0.935262338  0.56231264  2.1242791830  0.3720182728  0.718006182
## [368,]  2.492171120 -0.48928746  2.4676282836  1.9668068431 -0.727490529
## [369,] -0.327363502 -0.84626614  2.2688783371  0.9603180211 -0.407816836
## [370,] -1.468296601  0.18028669  1.6652393313  1.5773153771  0.412661443
## [371,]  0.644477407  1.35334644  2.6883609615  0.5712489712  0.440528158
## [372,]  4.369563022 -1.66481832  1.6865361527  0.4901972904  0.760040778
## [373,] -2.357052820 -1.26900605  1.5231357317  1.0301102498  0.074632682
## [374,]  0.718708019  0.22127710  1.0354060443  0.2583339391  1.891779073
## [375,]  1.391878059  0.98004221  1.7111474295 -0.7952838709  2.265775349
## [376,]  0.905097897 -0.22694710  2.1140189340  0.5476029310  0.603860387
## [377,]  3.157230391 -1.19754195  1.1484347290  1.0599855046  1.186962665
## [378,]  0.003135705 -0.90598915  1.6393299343 -1.1011824448  1.359035590
## [379,] -0.242056357 -0.73255189  1.7021620290 -0.1866470103  0.800865246
##                 PC6          PC7
##   [1,]  0.814428206 -0.107883916
##   [2,] -0.048912344 -0.099604504
##   [3,] -0.086507916 -0.138527863
##   [4,] -0.822748232  0.360506834
##   [5,] -0.108812986  0.078970882
##   [6,]  0.183797925  0.433343571
##   [7,]  0.008911379 -0.004657966
##   [8,]  0.543125568 -0.332707934
##   [9,] -0.752701863  0.056474342
##  [10,] -0.441826427 -1.924448799
##  [11,] -0.244944687  0.159851097
##  [12,]  0.206259597 -0.169273224
##  [13,]  0.163519054 -0.103667561
##  [14,]  0.132474346  0.108653816
##  [15,] -1.324055932 -0.183915616
##  [16,]  0.714919089  0.304537991
##  [17,] -0.647376538  0.365592105
##  [18,]  1.097596271 -0.377715183
##  [19,]  0.334391075 -0.234827285
##  [20,]  0.808587321 -0.200036177
##  [21,]  0.322170368 -0.166529357
##  [22,]  0.107803508  0.012805983
##  [23,] -0.332323319 -0.202474142
##  [24,]  0.995998868  0.201016672
##  [25,] -2.363493528  0.266625584
##  [26,] -0.813907073 -0.571488560
##  [27,] -2.160783056  0.281527887
##  [28,]  0.098479393  0.336756957
##  [29,]  0.004273460 -0.381406184
##  [30,] -0.044211599 -0.418300721
##  [31,] -0.128464996  0.054899611
##  [32,] -0.357344175  0.183909490
##  [33,] -0.597244606  0.289672968
##  [34,]  0.259235600  0.349194654
##  [35,] -0.236888897 -0.371166651
##  [36,] -0.249251785  0.050335461
##  [37,]  0.607590347 -0.462113845
##  [38,] -0.026797156  0.355817879
##  [39,]  0.166045669 -0.073826942
##  [40,] -0.162738506 -0.392300116
##  [41,] -0.522507663 -0.121724380
##  [42,]  0.067225848  0.209115377
##  [43,] -0.417780877 -0.474060203
##  [44,] -0.173878940 -0.457967209
##  [45,] -0.050403121 -0.134114068
##  [46,] -0.089979747 -0.491479393
##  [47,]  0.480573605 -0.072323181
##  [48,]  0.228887831  0.155522234
##  [49,] -0.489991807 -0.227097997
##  [50,] -0.606582969 -0.101166456
##  [51,]  0.577660866 -0.455756839
##  [52,]  0.585446120 -0.388137976
##  [53,]  0.734811073  1.561539615
##  [54,]  1.381511548  0.252947237
##  [55,]  0.358959045 -0.182311216
##  [56,]  0.207910788  0.078632864
##  [57,]  0.607774154 -0.281869942
##  [58,]  2.443161543  0.443513680
##  [59,]  0.206843192  0.253038172
##  [60,]  0.135499206  0.164773439
##  [61,]  0.648725932  0.351461678
##  [62,]  0.166486526  0.246682271
##  [63,] -0.513948300 -0.286040883
##  [64,]  1.163578265  0.263125274
##  [65,] -0.009862807  0.134046265
##  [66,] -0.730377136  0.337181681
##  [67,] -1.487448857 -0.149925371
##  [68,]  0.220853759  0.272493773
##  [69,] -0.588054260  0.260689981
##  [70,] -0.385273067  0.319508713
##  [71,] -0.175254751  1.897246402
##  [72,] -1.300330063 -0.404208363
##  [73,]  0.816322549 -0.225387244
##  [74,] -0.060212427  0.165026305
##  [75,] -1.649589162 -0.529795744
##  [76,]  0.569158827 -0.263377372
##  [77,] -0.165692949 -0.401192949
##  [78,]  0.043436354  0.440699177
##  [79,]  0.327782857  0.371732847
##  [80,]  0.016945132  0.140928440
##  [81,] -0.877693420 -0.271276638
##  [82,]  0.050656761  0.314869348
##  [83,]  0.024270266 -0.489647178
##  [84,] -0.428408376  0.144447332
##  [85,]  0.302353058  0.176709283
##  [86,] -0.930367776 -0.038966156
##  [87,]  0.206974359  1.518547012
##  [88,]  0.773220076  0.387655208
##  [89,] -0.057425863  0.311702214
##  [90,] -0.319492539 -0.104439493
##  [91,]  0.464021241 -0.182053564
##  [92,]  0.568469956  0.135273025
##  [93,] -0.637098352 -0.352179961
##  [94,] -0.897710356 -0.603436508
##  [95,] -0.302718373  0.134220300
##  [96,]  0.796303291 -0.453234619
##  [97,]  0.102248374 -0.373850042
##  [98,]  0.276775028 -0.386841666
##  [99,] -0.147547074 -2.150145655
## [100,]  0.522935395 -0.336156710
## [101,] -1.015284422 -0.131608533
## [102,]  0.945355253  0.288290374
## [103,]  0.240503118  0.089283023
## [104,]  0.040655927 -0.326527188
## [105,]  0.156719385 -0.425753859
## [106,] -0.378077108 -0.375663969
## [107,]  0.617517671 -0.018331347
## [108,] -0.140360458  0.357139007
## [109,] -0.369058053 -0.363453154
## [110,]  1.367651547 -0.052494633
## [111,] -0.245674045  0.171961839
## [112,] -0.288279169 -0.437854120
## [113,]  0.654181743  0.335734007
## [114,]  0.430171258  0.242838061
## [115,] -0.609725681 -0.399796060
## [116,] -0.153071461  0.293451739
## [117,]  0.435961104  0.348338090
## [118,] -1.122876095  0.371334968
## [119,]  0.128953459 -0.002950892
## [120,]  0.454338848 -0.320002000
## [121,] -0.393321862  0.002244332
## [122,]  0.694427666 -1.776651924
## [123,] -1.480360092  0.237363812
## [124,]  0.563305776  0.061168635
## [125,]  0.789672355  0.182676841
## [126,]  0.657430786  0.151394277
## [127,]  0.052053042 -0.260063201
## [128,] -0.509971776  0.300299579
## [129,] -0.514688913  0.253498821
## [130,] -0.230653718  0.334001823
## [131,]  0.234492897  0.070164155
## [132,] -0.509623760  0.211476411
## [133,] -0.508032972  0.218820879
## [134,] -0.584676128  0.432040803
## [135,] -0.599512631  0.114578050
## [136,]  0.742555446  0.264941606
## [137,]  0.215593238 -0.296341138
## [138,]  0.814373445 -0.463329220
## [139,] -0.705236433  0.235224585
## [140,] -0.240819937  0.128832004
## [141,] -0.738265473  0.045748305
## [142,] -0.516065685  0.423763629
## [143,]  1.032627703  0.255695270
## [144,]  1.011640901 -0.046612704
## [145,]  1.036057364 -0.116502648
## [146,]  0.238779557 -0.094409829
## [147,]  0.093045275 -0.025943269
## [148,] -0.018285774  0.063985702
## [149,] -0.821062597  0.316957388
## [150,] -0.051433159 -0.325889337
## [151,]  0.240258258  0.157499206
## [152,]  0.244055313 -0.484326189
## [153,]  0.321762278  0.347844280
## [154,] -0.688031620  0.275674116
## [155,]  0.052870105  0.278750325
## [156,]  0.259394959  0.994613529
## [157,]  0.384573263  0.255112420
## [158,] -0.647167228  0.095523521
## [159,] -0.447355557 -0.367626528
## [160,] -1.037268876 -0.081314104
## [161,]  0.685349399 -0.373379228
## [162,] -0.574402441 -0.041182433
## [163,] -0.812645636  0.354791023
## [164,]  0.259528832  0.196856471
## [165,] -0.112837907 -0.422270866
## [166,]  0.128000241 -0.175939627
## [167,] -0.895512404  0.337192272
## [168,] -0.711019273 -0.814804273
## [169,]  0.218357219 -0.033915231
## [170,] -0.078144315  0.263676922
## [171,]  0.789052948  0.069697557
## [172,]  0.334044498  0.095799549
## [173,] -0.466799910  0.182242801
## [174,] -0.409218588  0.105315011
## [175,]  0.475675622  0.157100174
## [176,]  0.631970192 -0.312887516
## [177,] -0.842796008  0.184336624
## [178,] -0.521271064  0.253595738
## [179,] -0.195535437 -0.489681481
## [180,] -0.238968439  0.339455192
## [181,]  1.224469205  0.162311433
## [182,]  0.896759582 -0.187133556
## [183,] -0.369525579  0.051355060
## [184,] -1.133798661 -0.032484936
## [185,] -0.525703790  0.938668397
## [186,]  0.115704613 -0.308573611
## [187,] -0.330011041  0.052298230
## [188,]  0.252831722 -0.344500770
## [189,]  0.478267892 -0.411989559
## [190,]  0.108389410  0.270176494
## [191,]  0.320051815 -0.452948617
## [192,] -0.927317654  0.050049377
## [193,]  0.049967323  0.232020283
## [194,] -0.322439393 -0.332013839
## [195,] -0.576452643  0.112196595
## [196,] -0.426323754  0.064708147
## [197,]  0.577314293 -0.090994712
## [198,] -0.220002645 -0.145293651
## [199,]  1.007924154 -0.238873759
## [200,] -0.144916255 -0.256657796
## [201,]  0.222523935 -0.327353336
## [202,]  0.143637470 -0.384469784
## [203,] -0.685873899  0.077706170
## [204,] -0.684433914 -0.555287379
## [205,] -0.739601209  0.286336764
## [206,] -0.391145161  0.071275723
## [207,]  1.031184262 -0.071523474
## [208,]  0.422795216 -0.361912372
## [209,]  0.232252275 -0.321891385
## [210,]  0.132512399 -2.194006418
## [211,]  0.300407101  0.236278993
## [212,] -0.181056517 -0.655811887
## [213,] -2.264161275  0.013076856
## [214,] -0.146543860  0.258375350
## [215,] -0.914443039 -0.156858207
## [216,]  0.163052914  0.373094641
## [217,]  0.735902331  0.298434341
## [218,]  0.858016687 -0.410620478
## [219,] -0.698483214  0.291328307
## [220,] -1.702108557 -0.103054608
## [221,] -0.570947694 -0.064210529
## [222,]  0.103014117 -0.154551366
## [223,]  0.032313480  0.248280548
## [224,] -0.245512705 -0.395034205
## [225,] -0.795643311  0.316447811
## [226,]  0.757677018  0.355289619
## [227,]  0.112343498 -0.370694673
## [228,]  2.840081863 -0.472760040
## [229,] -0.117535015  0.251369052
## [230,] -0.123999729 -0.103219333
## [231,]  0.620151206 -0.398726087
## [232,] -1.258499518  0.031686285
## [233,]  0.508788077  0.031702502
## [234,] -0.730990134  0.229897436
## [235,] -0.131943879  0.351750927
## [236,]  0.930178961  0.218030323
## [237,] -1.155883577 -0.406938969
## [238,]  0.421016873 -0.245001577
## [239,] -0.919968833  0.339656927
## [240,] -0.475488496  0.136247856
## [241,]  1.761754259  0.029538972
## [242,]  1.222218060 -0.319429458
## [243,] -0.387563364 -0.168870331
## [244,] -1.348003518 -0.078702906
## [245,] -0.096908019  0.116533237
## [246,]  0.123274608  0.151123503
## [247,] -0.489960306  0.098338159
## [248,]  0.676566199 -0.339944716
## [249,]  0.072286130  0.262572292
## [250,] -0.203974262  0.359934672
## [251,] -0.962511140  0.447744836
## [252,]  0.026617023  0.293556296
## [253,] -0.615601226 -0.158798853
## [254,]  0.165313198  0.013008846
## [255,]  1.432136191  1.223639292
## [256,]  0.483977624 -0.346520349
## [257,] -0.153805545  0.159416002
## [258,] -0.327177547  0.145372443
## [259,]  0.927279628  0.136024542
## [260,]  0.347645497 -0.209884830
## [261,]  0.229700925 -0.104543344
## [262,] -0.158104523 -0.333049945
## [263,] -0.057284357 -0.187261115
## [264,] -1.002026891  0.117204649
## [265,]  1.233710972  0.172803485
## [266,] -0.621049559 -0.266818669
## [267,]  1.556396291  0.244375096
## [268,] -0.067622566 -0.072725103
## [269,] -0.175077307 -0.498801012
## [270,] -0.666813685  0.155867363
## [271,] -0.136040334 -0.327359471
## [272,]  0.778990215 -0.465309183
## [273,]  0.693723928 -0.130197667
## [274,] -1.468695169  0.266972231
## [275,]  0.429361577 -0.105547847
## [276,] -0.773390730 -0.033260132
## [277,]  0.336674762  1.064820895
## [278,] -0.300804152  0.703841870
## [279,] -0.238262975  0.450690335
## [280,]  0.395969716 -0.242043012
## [281,]  0.109021256  0.138748544
## [282,] -0.037963898  0.268885486
## [283,] -0.373873694 -0.512209208
## [284,] -0.029714459 -0.403875221
## [285,]  0.426625104  0.228719436
## [286,] -0.362288537  0.223311049
## [287,]  0.384277844 -0.106878993
## [288,] -1.421668738  0.046595855
## [289,] -2.984199195  0.075859453
## [290,]  1.319916883  2.001667923
## [291,]  2.046793198 -0.269649215
## [292,]  0.392813424  0.303644436
## [293,]  0.021688217  0.270137554
## [294,] -0.049144987 -0.046060227
## [295,] -1.011855498 -0.955345258
## [296,] -0.175912153  0.163389864
## [297,] -0.811118093  0.416648260
## [298,] -0.340865035 -0.224224889
## [299,]  0.466059600  0.157785884
## [300,]  0.558304051 -0.192471657
## [301,]  0.750653613  0.459663166
## [302,]  1.122352945 -0.276052847
## [303,]  1.078964668  0.210264826
## [304,]  0.426300512  0.141513828
## [305,]  0.810547774  0.065859782
## [306,] -0.181814543  1.697357273
## [307,]  0.699571022 -0.449062901
## [308,]  0.145047367 -0.510569761
## [309,] -0.335948519 -0.163889426
## [310,]  0.695110312 -0.089730044
## [311,] -0.421019920 -0.164631917
## [312,] -0.328893323  0.125575320
## [313,] -0.600269847  0.190331629
## [314,] -0.800239413 -0.264240505
## [315,] -0.079057717  0.438769076
## [316,] -0.386407008 -0.406110560
## [317,]  1.041640267  0.390303651
## [318,] -0.189857024  0.234508553
## [319,] -1.090183460  0.762300322
## [320,]  0.386282802 -0.239807387
## [321,]  0.134404520  0.127105246
## [322,]  0.366835108  0.216268360
## [323,]  0.342909111  0.372677157
## [324,] -0.254516438 -0.193658003
## [325,]  0.533845103 -0.328861238
## [326,] -0.465612342 -0.352871158
## [327,] -0.163023346  0.003333250
## [328,] -0.798713796  0.164392019
## [329,]  0.481838526 -1.448359073
## [330,] -1.226111979 -0.366016068
## [331,]  1.020308661  0.044230674
## [332,]  1.056394345 -0.394589336
## [333,] -1.007313550  0.374213944
## [334,]  0.492601789  0.244276984
## [335,]  0.411613111 -0.135788109
## [336,] -0.280767946  0.263720304
## [337,]  0.160862506 -0.192753984
## [338,]  0.791036742  0.678047807
## [339,]  0.126529280  0.120748763
## [340,]  0.262317102 -0.088849352
## [341,]  0.041119374 -0.483927739
## [342,] -0.678266870 -0.258446039
## [343,]  1.445310485  0.036985630
## [344,] -0.175915279  0.027902348
## [345,]  0.564004554 -0.503273137
## [346,] -1.123890798 -0.049820336
## [347,] -0.529962184  0.213624141
## [348,]  0.448319463 -0.109057231
## [349,]  0.164185074 -0.178027089
## [350,]  0.343302649  0.295711308
## [351,]  1.064600476 -0.399557062
## [352,]  0.402428026 -0.264910522
## [353,] -0.039235833  0.080955691
## [354,] -0.401278508  0.033682397
## [355,] -0.845062983  0.190359077
## [356,]  0.916027349 -0.545821754
## [357,]  0.946629462  0.303161216
## [358,] -0.119192699 -0.421977595
## [359,] -0.474603729  0.232244290
## [360,]  0.620269650  0.217072532
## [361,]  0.290272477 -0.446292100
## [362,]  0.807055770  0.427223893
## [363,]  1.725250067  0.275888197
## [364,] -0.573212533 -0.177662617
## [365,] -0.242829260  0.310782840
## [366,] -0.025556816  0.310309937
## [367,] -0.369535370  0.246732337
## [368,]  0.794924538  0.929445109
## [369,] -0.044906053  0.144701045
## [370,] -0.730353345  0.202922032
## [371,]  0.105639703 -0.429239913
## [372,] -0.245135971  0.186120856
## [373,] -0.823120736  0.174853047
## [374,]  1.126518713 -0.084801083
## [375,] -0.200011773 -0.549385252
## [376,] -1.229143214  0.135743929
## [377,] -0.299503313  0.743333133
## [378,]  0.410392839 -0.361555114
## [379,]  0.837670932 -0.196874004
plot(Cancer_pca)

#get the original value of the data based on PCA
center <- Cancer_pca$center
scale <- Cancer_pca$scale
new_Cancer <- as.matrix(Cancer[,-1])
new_Cancer
##        Age Stage Tumor Size Regional Node Examined Reginol Node Positive
##   [1,]  68     1          4                     24                     1
##   [2,]  50     2         35                     14                     5
##   [3,]  58     3         63                     14                     7
##   [4,]  58     1         18                      2                     1
##   [5,]  47     2         41                      3                     1
##   [6,]  51     1         20                     18                     2
##   [7,]  51     1          8                     11                     1
##   [8,]  40     2         30                      9                     1
##   [9,]  40     4        103                     20                    18
##  [10,]  69     4         32                     21                    12
##  [11,]  68     1         13                      9                     1
##  [12,]  46     3         59                     11                     3
##  [13,]  65     2         35                     13                     3
##  [14,]  48     1         15                     23                     7
##  [15,]  62     2         35                     16                    14
##  [16,]  61     1         19                     20                     1
##  [17,]  56     2         46                      1                     1
##  [18,]  43     2         24                     22                     1
##  [19,]  48     2         25                     16                     1
##  [20,]  60     2         29                     20                     1
##  [21,]  48     2         30                     15                     2
##  [22,]  57     2         40                     15                     5
##  [23,]  55     2         29                      4                     1
##  [24,]  48     3         70                     18                     1
##  [25,]  62     1         20                     26                    22
##  [26,]  63     2         22                     31                    17
##  [27,]  48     2         50                     25                    23
##  [28,]  46     1         17                     14                     1
##  [29,]  57     2         25                     14                     4
##  [30,]  66     2         21                     10                     1
##  [31,]  47     2         40                      3                     1
##  [32,]  53     1         15                      5                     1
##  [33,]  59     1         15                      6                     1
##  [34,]  60     1         20                     19                     3
##  [35,]  46     2         30                     19                    10
##  [36,]  51     1         10                      9                     2
##  [37,]  54     2         27                     21                     6
##  [38,]  51     1         18                     14                     2
##  [39,]  49     2         35                     10                     2
##  [40,]  51     2         23                     15                     5
##  [41,]  57     3         70                     12                    12
##  [42,]  64     1         17                     12                     2
##  [43,]  62     2         21                      2                     1
##  [44,]  53     2         23                     15                     6
##  [45,]  55     1          5                     11                     2
##  [46,]  66     3         51                     10                     5
##  [47,]  42     1          9                     15                     2
##  [48,]  62     1         15                     12                     1
##  [49,]  53     2         32                     16                     9
##  [50,]  69     1          5                      8                     3
##  [51,]  37     2         23                     17                     3
##  [52,]  69     3         55                      9                     1
##  [53,]  60     3        120                      7                     1
##  [54,]  63     3         77                     20                     2
##  [55,]  57     1          2                     16                     1
##  [56,]  55     1         11                     13                     1
##  [57,]  62     2         25                     19                     1
##  [58,]  50     1         18                     49                     1
##  [59,]  50     1         15                     15                     1
##  [60,]  55     1         12                     17                     2
##  [61,]  56     1         18                     24                     2
##  [62,]  51     1         17                     12                     1
##  [63,]  42     2         26                      1                     1
##  [64,]  59     3         75                     20                     2
##  [65,]  67     1         13                     16                     3
##  [66,]  46     1         15                      5                     1
##  [67,]  31     3         70                     23                    23
##  [68,]  40     1         15                     20                     3
##  [69,]  58     1         15                      5                     1
##  [70,]  52     1         17                     12                     3
##  [71,]  49     3        130                     12                     8
##  [72,]  64     2         34                     24                    20
##  [73,]  31     2         30                     16                     1
##  [74,]  66     1         10                     15                     1
##  [75,]  67     2         22                     19                    16
##  [76,]  56     3         55                     13                     1
##  [77,]  66     2         25                     11                     4
##  [78,]  42     2         50                      7                     1
##  [79,]  51     2         50                      9                     1
##  [80,]  68     1         15                      9                     1
##  [81,]  53     2         30                     21                    13
##  [82,]  67     1         20                     10                     1
##  [83,]  66     2         22                      9                     2
##  [84,]  53     1         15                      2                     1
##  [85,]  51     1         15                     13                     1
##  [86,]  46     2         40                     12                    11
##  [87,]  48     3        120                      7                     5
##  [88,]  52     3         80                     10                     1
##  [89,]  55     1         17                     11                     1
##  [90,]  65     1          3                      9                     1
##  [91,]  53     3         60                      8                     1
##  [92,]  33     1         14                     15                     1
##  [93,]  63     2         26                      5                     4
##  [94,]  45     2         25                     21                    16
##  [95,]  59     1         12                     12                     3
##  [96,]  60     2         25                     17                     2
##  [97,]  50     2         30                      4                     2
##  [98,]  61     2         25                     10                     1
##  [99,]  50     4         24                      3                     3
## [100,]  68     2         27                     14                     1
## [101,]  38     3         70                     33                    24
## [102,]  47     1         16                     25                     1
## [103,]  39     2         45                      3                     1
## [104,]  57     2         27                      7                     1
## [105,]  52     2         23                     14                     3
## [106,]  60     2         25                      2                     1
## [107,]  54     2         40                     11                     1
## [108,]  68     1         20                     12                     2
## [109,]  38     2         21                      8                     2
## [110,]  63     2         36                     30                     3
## [111,]  61     1         14                     15                     4
## [112,]  37     3         51                      3                     3
## [113,]  46     2         50                     34                    10
## [114,]  45     2         45                     14                     2
## [115,]  54     3         51                      6                     5
## [116,]  53     1         19                     12                     3
## [117,]  50     3         76                      9                     1
## [118,]  69     1         20                     16                     9
## [119,]  48     2         35                     15                     3
## [120,]  53     2         27                     15                     2
## [121,]  67     2         35                      7                     2
## [122,]  43     4         35                     15                     3
## [123,]  50     2         50                     16                    16
## [124,]  59     2         38                     23                     4
## [125,]  53     1         15                     23                     2
## [126,]  62     1         17                     16                     1
## [127,]  39     2         25                     13                     2
## [128,]  59     1         19                      3                     1
## [129,]  56     1         15                      8                     2
## [130,]  45     1         18                     13                     3
## [131,]  60     1         11                     14                     1
## [132,]  50     2         45                     10                     6
## [133,]  58     1         12                      8                     1
## [134,]  50     1         20                      5                     1
## [135,]  55     2         45                      8                     7
## [136,]  37     1         18                     28                     5
## [137,]  46     2         25                     12                     1
## [138,]  65     2         21                     20                     1
## [139,]  61     2         49                     14                    10
## [140,]  52     3         70                     18                     9
## [141,]  54     1          7                      4                     1
## [142,]  36     1         19                     13                     4
## [143,]  49     1         17                     24                     1
## [144,]  62     2         38                     23                     3
## [145,]  54     2         34                     20                     1
## [146,]  61     2         30                     15                     1
## [147,]  46     1          4                     18                     2
## [148,]  38     3         72                     13                     8
## [149,]  66     1         18                      1                     1
## [150,]  59     2         25                     13                     3
## [151,]  38     1          9                     18                     1
## [152,]  67     2         21                     14                     2
## [153,]  60     1         20                     15                     1
## [154,]  61     1         15                     14                     5
## [155,]  67     1         18                     14                     2
## [156,]  69     3        100                     16                     6
## [157,]  47     1         17                     15                     1
## [158,]  39     1          7                      6                     1
## [159,]  53     2         24                      2                     1
## [160,]  55     2         43                     14                    14
## [161,]  59     2         30                     18                     4
## [162,]  53     1          7                      3                     1
## [163,]  59     1         18                      2                     1
## [164,]  57     1         12                     20                     2
## [165,]  61     2         25                     16                     6
## [166,]  68     3         62                      3                     1
## [167,]  54     1         20                     12                     7
## [168,]  37     4         70                     24                    17
## [169,]  48     2         37                      8                     1
## [170,]  53     1         13                     14                     1
## [171,]  69     2         40                     20                     2
## [172,]  63     3         70                     11                     3
## [173,]  49     1         12                      9                     2
## [174,]  63     1          9                      9                     1
## [175,]  60     1         10                     24                     2
## [176,]  41     3         55                     11                     1
## [177,]  59     1         18                     17                    10
## [178,]  43     1         15                      7                     2
## [179,]  52     2         25                     31                    14
## [180,]  61     2         50                     11                     5
## [181,]  60     1         10                     32                     1
## [182,]  61     2         30                     23                     2
## [183,]  63     1         13                      3                     1
## [184,]  48     2         40                     15                    13
## [185,]  51     3        100                     14                    11
## [186,]  66     2         25                     14                     2
## [187,]  68     3         68                      3                     3
## [188,]  58     2         25                     14                     2
## [189,]  62     2         23                     34                     9
## [190,]  46     1         15                     14                     1
## [191,]  58     2         22                     12                     1
## [192,]  60     1          7                      2                     1
## [193,]  62     1         16                     19                     4
## [194,]  53     2         24                      5                     1
## [195,]  42     3         75                     16                    13
## [196,]  63     1         11                      5                     1
## [197,]  55     2         35                     16                     2
## [198,]  50     3         60                     10                     5
## [199,]  52     2         30                     22                     2
## [200,]  47     2         25                     11                     2
## [201,]  55     2         25                     14                     2
## [202,]  60     2         25                     16                     4
## [203,]  66     1         12                      1                     1
## [204,]  50     2         25                     17                    12
## [205,]  64     1         17                      2                     1
## [206,]  67     1         11                      6                     1
## [207,]  56     2         32                     24                     1
## [208,]  60     2         21                     18                     1
## [209,]  56     2         25                     12                     1
## [210,]  48     4         19                      6                     1
## [211,]  44     3         75                     11                     4
## [212,]  37     3         52                     17                    12
## [213,]  52     1          9                     18                    17
## [214,]  63     1         17                      9                     1
## [215,]  54     2         35                     10                     9
## [216,]  63     3         85                      4                     4
## [217,]  44     2         50                     12                     1
## [218,]  68     3         51                     17                     1
## [219,]  64     1         18                      4                     2
## [220,]  50     3         75                     27                    27
## [221,]  55     3         72                     14                    13
## [222,]  66     2         35                     20                     7
## [223,]  46     1         12                     18                     2
## [224,]  43     2         23                      9                     3
## [225,]  43     1         16                      2                     1
## [226,]  43     1         16                     27                     2
## [227,]  59     3         57                     20                     9
## [228,]  55     3         50                     42                     1
## [229,]  61     1         17                      9                     1
## [230,]  66     2         32                     15                     4
## [231,]  55     2         21                     19                     1
## [232,]  65     1         11                      7                     7
## [233,]  69     2         40                     22                     5
## [234,]  59     1         15                      2                     1
## [235,]  63     1         17                     15                     2
## [236,]  68     1         14                     26                     1
## [237,]  48     3         60                     26                    21
## [238,]  61     3         55                     12                     1
## [239,]  43     4        120                     28                    26
## [240,]  44     1         11                      8                     2
## [241,]  47     2         39                     29                     1
## [242,]  52     2         23                     30                     2
## [243,]  69     2         28                      9                     2
## [244,]  39     2         37                     18                    15
## [245,]  43     2         40                     15                     5
## [246,]  64     1          9                     18                     1
## [247,]  66     1          8                      9                     1
## [248,]  45     2         28                     18                     3
## [249,]  37     1         15                     15                     2
## [250,]  50     1         17                     11                     1
## [251,]  40     2         50                      6                     6
## [252,]  52     2         48                      5                     1
## [253,]  41     2         30                      2                     2
## [254,]  32     3         68                     13                     6
## [255,]  65     3        110                     19                     2
## [256,]  67     2         23                     20                     2
## [257,]  57     1         12                     13                     2
## [258,]  63     1         13                      7                     1
## [259,]  42     2         40                     20                     1
## [260,]  57     2         30                     12                     1
## [261,]  42     1          9                     11                     2
## [262,]  46     2         22                      9                     1
## [263,]  47     2         30                      9                     2
## [264,]  67     1         12                      3                     3
## [265,]  67     1         10                     33                     1
## [266,]  65     2         25                      3                     1
## [267,]  65     1         16                     33                     1
## [268,]  33     3         65                      3                     3
## [269,]  64     2         22                      4                     1
## [270,]  66     1         17                     20                    10
## [271,]  34     3         60                     13                     9
## [272,]  55     2         22                     20                     2
## [273,]  47     2         35                     18                     3
## [274,]  58     1         18                      9                     9
## [275,]  38     2         34                     11                     1
## [276,]  57     1          6                      2                     1
## [277,]  65     3        105                      4                     2
## [278,]  52     3        100                     23                    17
## [279,]  67     1         20                     14                     2
## [280,]  57     3         57                     14                     3
## [281,]  61     1         10                     16                     1
## [282,]  45     1         17                     12                     2
## [283,]  50     2         25                     18                    10
## [284,]  50     2         21                     12                     2
## [285,]  53     2         45                     14                     2
## [286,]  54     2         50                      7                     6
## [287,]  58     2         35                     13                     2
## [288,]  56     2         38                     12                    11
## [289,]  68     1         16                     30                    28
## [290,]  41     3        140                     41                    15
## [291,]  61     2         25                     39                     1
## [292,]  65     1         18                     17                     1
## [293,]  69     1         18                     11                     1
## [294,]  43     2         34                     19                     6
## [295,]  47     4         65                     14                    14
## [296,]  67     1         13                     10                     1
## [297,]  45     1         20                      1                     1
## [298,]  65     2         29                     11                     4
## [299,]  53     1         10                     21                     1
## [300,]  67     3         62                     13                     3
## [301,]  43     2         50                     18                     1
## [302,]  47     2         29                     23                     2
## [303,]  48     1         15                     30                     3
## [304,]  62     1         15                     46                    14
## [305,]  68     2         42                     25                     5
## [306,]  57     3        130                     10                    10
## [307,]  40     2         21                     22                     3
## [308,]  56     3         51                     10                     4
## [309,]  52     2         30                      4                     1
## [310,]  40     2         35                     19                     3
## [311,]  51     2         31                      4                     2
## [312,]  67     1         14                     15                     5
## [313,]  54     1         15                     14                     6
## [314,]  56     3         60                     27                    17
## [315,]  48     1         20                     12                     1
## [316,]  57     2         22                      4                     1
## [317,]  47     3         80                     14                     1
## [318,]  54     1         15                     14                     3
## [319,]  41     3        100                     28                    23
## [320,]  65     2         30                     12                     1
## [321,]  58     1          8                     18                     1
## [322,]  38     1         15                     15                     1
## [323,]  38     3         80                      8                     3
## [324,]  60     2         30                     19                     7
## [325,]  58     2         25                     16                     1
## [326,]  63     2         24                     15                     6
## [327,]  53     2         35                     14                     4
## [328,]  43     1         12                      1                     1
## [329,]  60     4         45                      9                     1
## [330,]  60     2         25                     10                     9
## [331,]  47     2         35                     24                     1
## [332,]  48     2         28                     19                     2
## [333,]  59     1         17                      6                     3
## [334,]  56     1         15                     19                     1
## [335,]  53     2         32                     13                     1
## [336,]  48     1         15                     11                     2
## [337,]  52     3         60                      4                     1
## [338,]  61     3         90                     13                     2
## [339,]  66     1         11                     19                     3
## [340,]  45     2         37                     13                     4
## [341,]  52     2         21                     12                     3
## [342,]  67     1          2                     19                     9
## [343,]  40     3         70                     17                     1
## [344,]  50     1          8                      9                     1
## [345,]  65     2         22                     23                     5
## [346,]  55     2         40                     12                    12
## [347,]  47     1         13                      5                     1
## [348,]  49     2         32                     16                     2
## [349,]  53     1          5                     29                     9
## [350,]  53     1         18                     17                     2
## [351,]  44     3         52                     24                     4
## [352,]  54     2         31                     16                     4
## [353,]  51     1         14                      6                     1
## [354,]  46     1          7                      7                     1
## [355,]  47     1         12                      1                     1
## [356,]  68     2         21                     18                     1
## [357,]  50     1         20                     23                     2
## [358,]  67     2         26                      5                     2
## [359,]  47     1         16                      3                     1
## [360,]  68     1         15                     20                     1
## [361,]  55     2         25                     10                     2
## [362,]  47     1         20                     23                     1
## [363,]  56     3         80                     24                     3
## [364,]  51     2         30                      2                     2
## [365,]  41     1         16                     11                     2
## [366,]  67     1         20                     16                     4
## [367,]  58     1         17                     19                     7
## [368,]  67     3        100                     25                     8
## [369,]  63     2         41                     14                     4
## [370,]  69     1         16                     12                     6
## [371,]  59     2         25                     30                    11
## [372,]  44     4        108                     16                    14
## [373,]  65     1         12                      2                     1
## [374,]  48     2         38                     24                     4
## [375,]  39     2         24                     26                    13
## [376,]  55     2         45                     14                    13
## [377,]  50     3         98                     14                    12
## [378,]  39     2         25                     16                     3
## [379,]  49     2         30                     18                     1
##        Survival Months Sex
##   [1,]              60   0
##   [2,]              62   0
##   [3,]              75   0
##   [4,]              84   0
##   [5,]              50   0
##   [6,]              89   0
##   [7,]              54   0
##   [8,]              14   0
##   [9,]              70   0
##  [10,]              92   0
##  [11,]              64   0
##  [12,]              92   0
##  [13,]              56   0
##  [14,]              38   0
##  [15,]              64   0
##  [16,]              49   0
##  [17,]             105   0
##  [18,]              62   0
##  [19,]             107   0
##  [20,]              77   0
##  [21,]              81   0
##  [22,]              50   0
##  [23,]              78   0
##  [24,]             102   0
##  [25,]              98   0
##  [26,]              70   0
##  [27,]             102   0
##  [28,]              82   0
##  [29,]              64   0
##  [30,]              86   0
##  [31,]              52   0
##  [32,]              49   0
##  [33,]              90   0
##  [34,]              62   0
##  [35,]              31   0
##  [36,]              77   1
##  [37,]              37   1
##  [38,]             103   1
##  [39,]              82   1
##  [40,]             105   1
##  [41,]              42   1
##  [42,]              61   1
##  [43,]              86   1
##  [44,]              84   1
##  [45,]              63   1
##  [46,]              90   1
##  [47,]              39   1
##  [48,]              59   1
##  [49,]              82   1
##  [50,]              82   1
##  [51,]              71   1
##  [52,]              71   1
##  [53,]              86   1
##  [54,]              70   1
##  [55,]              74   1
##  [56,]              73   1
##  [57,]              91   0
##  [58,]             106   0
##  [59,]              73   0
##  [60,]              77   0
##  [61,]              80   0
##  [62,]              49   0
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##  [76,]              95   0
##  [77,]              79   1
##  [78,]             106   1
##  [79,]              81   1
##  [80,]              55   1
##  [81,]             101   1
##  [82,]              65   1
##  [83,]              72   1
##  [84,]              55   1
##  [85,]              65   1
##  [86,]              71   1
##  [87,]              82   1
##  [88,]              84   1
##  [89,]              95   1
##  [90,]              95   1
##  [91,]              91   1
##  [92,]              57   1
##  [93,]              87   1
##  [94,]              40   1
##  [95,]              91   1
##  [96,]              50   1
##  [97,]              25   1
##  [98,]              73   1
##  [99,]              63   0
## [100,]              50   0
## [101,]              54   0
## [102,]              73   0
## [103,]               8   0
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## [106,]              58   0
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## [110,]              61   0
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## [119,]              91   0
## [120,]              57   0
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## [123,]              62   0
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## [142,]             102   0
## [143,]              50   0
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## [146,]             107   0
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## [148,]              52   0
## [149,]              69   0
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## [155,]              56   0
## [156,]              91   0
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## [159,]              71   0
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## [174,]              87   0
## [175,]              96   0
## [176,]              74   0
## [177,]              47   0
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## [179,]              55   0
## [180,]              64   0
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## [182,]              74   0
## [183,]              23   0
## [184,]              60   0
## [185,]              85   0
## [186,]              86   0
## [187,]              81   0
## [188,]              71   0
## [189,]              90   0
## [190,]              79   0
## [191,]              60   0
## [192,]              89   0
## [193,]              66   0
## [194,]              84   0
## [195,]              55   0
## [196,]              50   0
## [197,]              55   0
## [198,]              98   0
## [199,]              53   0
## [200,]             103   0
## [201,]              77   0
## [202,]              63   0
## [203,]              45   0
## [204,]              25   0
## [205,]              68   0
## [206,]              53   0
## [207,]              91   0
## [208,]             105   0
## [209,]              76   0
## [210,]              94   0
## [211,]              71   0
## [212,]              15   0
## [213,]             106   0
## [214,]              56   0
## [215,]              56   0
## [216,]              16   0
## [217,]              31   0
## [218,]              85   0
## [219,]              62   0
## [220,]              23   0
## [221,]              24   0
## [222,]              50   0
## [223,]             107   0
## [224,]              76   0
## [225,]              87   0
## [226,]             101   0
## [227,]              60   0
## [228,]              66   0
## [229,]              53   0
## [230,]              93   0
## [231,]              90   0
## [232,]              59   0
## [233,]              58   0
## [234,]              68   0
## [235,]              94   0
## [236,]              72   0
## [237,]              53   0
## [238,]             103   0
## [239,]              16   0
## [240,]              77   0
## [241,]              49   0
## [242,]              99   0
## [243,]             107   0
## [244,]              81   0
## [245,]              87   0
## [246,]             103   0
## [247,]              96   0
## [248,]              40   0
## [249,]              78   0
## [250,]              92   0
## [251,]             106   0
## [252,]              54   0
## [253,]              85   0
## [254,]              69   0
## [255,]              51   0
## [256,]              93   0
## [257,]              76   0
## [258,]              58   0
## [259,]              79   0
## [260,]              63   0
## [261,]               7   0
## [262,]             104   0
## [263,]              74   0
## [264,]              67   0
## [265,]              98   0
## [266,]             100   0
## [267,]              58   0
## [268,]              61   0
## [269,]              45   0
## [270,]              48   0
## [271,]              40   0
## [272,]              57   0
## [273,]              42   0
## [274,]              76   0
## [275,]              55   0
## [276,]              68   0
## [277,]              49   0
## [278,]              16   0
## [279,]              99   0
## [280,]              88   0
## [281,]              87   0
## [282,]              60   0
## [283,]              34   0
## [284,]              92   0
## [285,]              65   0
## [286,]              23   0
## [287,]              50   0
## [288,]             107   0
## [289,]              92   0
## [290,]              51   0
## [291,]              92   0
## [292,]              61   0
## [293,]              50   0
## [294,]              95   0
## [295,]              97   0
## [296,]              65   0
## [297,]              81   0
## [298,]              81   0
## [299,]              92   0
## [300,]              53   0
## [301,]              91   0
## [302,]              49   0
## [303,]              61   0
## [304,]              74   0
## [305,]              48   0
## [306,]              37   0
## [307,]              75   0
## [308,]              57   0
## [309,]              81   0
## [310,]              56   0
## [311,]              73   0
## [312,]              53   0
## [313,]              68   0
## [314,]              94   0
## [315,]              88   0
## [316,]              79   0
## [317,]              63   0
## [318,]              74   0
## [319,]              57   0
## [320,]              53   0
## [321,]             104   0
## [322,]              57   0
## [323,]              63   0
## [324,]              90   0
## [325,]              73   0
## [326,]              94   0
## [327,]              98   0
## [328,]              74   0
## [329,]              89   0
## [330,]              89   0
## [331,]             100   0
## [332,]              16   0
## [333,]             107   0
## [334,]              70   0
## [335,]              68   0
## [336,]              81   0
## [337,]              67   0
## [338,]              67   0
## [339,]              97   1
## [340,]              60   1
## [341,]              86   1
## [342,]              75   1
## [343,]              59   1
## [344,]              87   1
## [345,]              75   1
## [346,]              72   1
## [347,]             102   1
## [348,]             101   1
## [349,]              68   1
## [350,]              80   1
## [351,]             104   1
## [352,]              61   1
## [353,]              41   1
## [354,]             100   1
## [355,]             105   1
## [356,]              57   1
## [357,]              59   1
## [358,]              54   1
## [359,]              76   1
## [360,]              82   1
## [361,]              53   1
## [362,]             102   1
## [363,]              47   1
## [364,]             100   1
## [365,]             107   1
## [366,]              73   1
## [367,]              91   1
## [368,]              92   1
## [369,]             107   1
## [370,]              85   1
## [371,]              89   1
## [372,]              71   1
## [373,]             102   1
## [374,]              49   1
## [375,]              59   1
## [376,]              90   1
## [377,]              57   1
## [378,]              85   1
## [379,]              86   1
drop(scale(new_Cancer,center=center, scale=scale)%*%Cancer_pca$rotation[,1])
##   [1] -1.441559363  0.466697152  1.724644704 -1.727412749  0.084534880
##   [6] -0.987174108 -1.289312885  0.457476281  5.013544810  1.966110970
##  [11] -1.709742154  1.323214712 -0.047344848 -0.023379894  1.042993427
##  [16] -0.954171084 -0.510183493  0.248390384 -0.386424810 -0.212235416
##  [21]  0.001291199  0.547237523 -0.581794885  1.484574719  0.730385134
##  [26]  1.384044724  2.503197607 -1.094732396 -0.040233637 -0.913495245
##  [31]  0.044817272 -1.310023914 -1.750326793 -0.860691537  1.293140200
##  [36] -1.575412171  0.505620687 -1.445729993 -0.240634131 -0.335231355
##  [41]  2.392046521 -1.496209472 -1.238156754 -0.122858339 -1.614959830
##  [46]  0.653344872 -0.903132282 -1.570956435  0.407142180 -2.095133885
##  [51]  0.145196356  0.438754344  2.005777230  1.526981600 -1.762004433
##  [56] -1.584099552 -0.496130040 -0.310631363 -1.133478035 -1.203472671
##  [61] -0.899762531 -1.006446958 -0.437812701  1.712300783 -1.263885916
##  [66] -1.604219653  4.488026052 -0.665172931 -1.668377900 -1.130422629
##  [71]  3.316812797  2.172380940  0.572326326 -1.827615023  0.720276568
##  [76]  0.849193077 -0.640547040 -0.095120639 -0.045215749 -1.769164273
##  [81]  0.718379560 -1.678008963 -0.895860760 -1.627068924 -1.331489281
##  [86]  0.909892498  2.680823986  1.353531002 -1.678967186 -2.304099591
##  [91]  0.741204117 -0.809147683 -0.790428226  1.549314451 -1.647991336
##  [96] -0.268121798 -0.103534223 -0.776307350  1.103113756 -0.409442426
## [101]  4.633190126 -0.740349810  0.704221402 -0.385204834 -0.068793640
## [106] -0.692576410  0.345220609 -1.364096376 -0.387521866  0.491580932
## [111] -1.087373932  1.210180885  1.869006469  0.492734252  0.889433533
## [116] -0.849321798  1.382626614 -0.876114257  0.129510618  0.006142764
## [121] -0.669636518  1.757579745  1.875711497  0.312604564 -0.681074580
## [126] -0.863182056 -0.118572831 -1.423953866 -1.441335172 -0.856545337
## [131] -1.307398005  0.585398503 -1.786207788 -1.427017695  0.756062138
## [136]  0.145449916 -0.274324587 -0.438129117  1.064299809  2.098096298
## [141] -1.849943605 -0.732556857 -0.608595125  0.505611656  0.247551976
## [146] -0.602802743 -1.272341157  2.651497970 -1.824221268 -0.352147008
## [151] -1.129437762 -0.549974224 -1.104925141 -1.260493668 -1.263788087
## [156]  2.182293451 -0.839030427 -1.567211240 -0.656681669  1.746317858
## [161]  0.576848393 -1.591129974 -1.734769097 -1.257058960  0.171012852
## [166]  0.763873736 -0.648233872  4.075761272  0.108096807 -1.498040609
## [171]  0.047885996  1.337596168 -1.358485537 -1.872027381 -1.311243234
## [176]  1.309706033 -0.190859319 -1.150520519  1.562083350  0.457663612
## [181] -1.138195339 -0.007740653 -1.442466409  1.401099127  3.044609211
## [186] -0.608848019  0.869481448 -0.300778748  0.636747830 -1.117892469
## [191] -0.433517740 -2.074508151 -0.943857160 -0.671437346  3.146400023
## [196] -1.646968799  0.194381857  1.355794604  0.342080981 -0.390007297
## [201] -0.278709707 -0.042662340 -1.773111892  1.250439359 -1.763032603
## [206] -1.734908122 -0.040455138 -0.686284826 -0.444359734  0.691490501
## [211]  2.007551495  2.980951104 -0.051043670 -1.433696923  0.663189426
## [216]  2.031410016  0.789603453  0.673484381 -1.540903396  4.811125983
## [221]  2.960210184  0.548555090 -1.203818787 -0.095903547 -1.447284264
## [226] -0.721456172  2.040310983  1.855207556 -1.362709085 -0.288896751
## [231] -0.418601999 -1.163850583  0.411132602 -1.693135796 -1.469262447
## [236] -1.241804213  3.689808324  0.637785394  6.741912903 -1.238593026
## [241]  0.823175506  0.046147404 -0.926653518  1.642861658  0.577872627
## [246] -1.754825326 -2.038325012  0.534102452 -0.778602587 -1.358620602
## [251]  0.552972231  0.160512695 -0.255760964  2.380048532  2.562080786
## [256] -0.556325503 -1.361977024 -1.604168388  0.453544197 -0.245088734
## [261] -0.586494355 -0.595783004 -0.098509308 -1.732739711 -1.312518153
## [266] -1.117483636 -0.802242010  1.779574174 -0.692885384 -0.296827034
## [271]  2.648459041 -0.009329958  0.636626889 -0.730329225  0.329127497
## [276] -1.859016837  2.011187895  4.387657320 -1.562200265  1.140064695
## [281] -1.592089421 -0.863852065  1.027169030 -0.436517354  0.337411799
## [286]  0.922063650  0.074518204  0.517903752  1.205633993  5.667322803
## [291]  0.117634314 -1.257776898 -1.442594978  0.581815447  3.192976367
## [296] -1.664428065 -1.381280799 -0.359580844 -1.295214100  1.275367360
## [301]  0.510190648  0.497692443 -0.360524908  0.680162177  0.651993920
## [306]  3.788964776  0.324102302  1.241627938 -0.511968929  0.718039754
## [311] -0.310163020 -1.033055205 -0.764852259  2.840965510 -1.178758036
## [316] -0.802177079  1.938258838 -1.084340607  5.007927517 -0.352175349
## [321] -1.645893870 -0.723629619  2.150497872  0.219479185 -0.347437994
## [326] -0.234908136  0.016559745 -1.467247701  1.154836707  0.020892606
## [331]  0.169022729  0.596241854 -1.658882001 -1.130296134 -0.114349001
## [336] -1.180178802  1.016962553  1.874901202 -1.674481841  0.347838749
## [341] -0.523787799 -1.191298001  1.808772263 -1.770065768 -0.206433118
## [346]  0.781356058 -1.821829245 -0.284787326 -0.436832085 -1.217940564
## [351]  1.408443279  0.076806137 -1.371613972 -1.864312777 -1.989259900
## [356] -0.666931670 -0.752021652 -0.799705965 -1.601727166 -1.657122757
## [361] -0.384493964 -1.117824446  2.156938592 -0.789754021 -1.380570918
## [366] -1.291560292 -0.935262338  2.492171120 -0.327363502 -1.468296601
## [371]  0.644477407  4.369563022 -2.357052820  0.718708019  1.391878059
## [376]  0.905097897  3.157230391  0.003135705 -0.242056357
predict(Cancer_pca)[,1]
##   [1] -1.441559363  0.466697152  1.724644704 -1.727412749  0.084534880
##   [6] -0.987174108 -1.289312885  0.457476281  5.013544810  1.966110970
##  [11] -1.709742154  1.323214712 -0.047344848 -0.023379894  1.042993427
##  [16] -0.954171084 -0.510183493  0.248390384 -0.386424810 -0.212235416
##  [21]  0.001291199  0.547237523 -0.581794885  1.484574719  0.730385134
##  [26]  1.384044724  2.503197607 -1.094732396 -0.040233637 -0.913495245
##  [31]  0.044817272 -1.310023914 -1.750326793 -0.860691537  1.293140200
##  [36] -1.575412171  0.505620687 -1.445729993 -0.240634131 -0.335231355
##  [41]  2.392046521 -1.496209472 -1.238156754 -0.122858339 -1.614959830
##  [46]  0.653344872 -0.903132282 -1.570956435  0.407142180 -2.095133885
##  [51]  0.145196356  0.438754344  2.005777230  1.526981600 -1.762004433
##  [56] -1.584099552 -0.496130040 -0.310631363 -1.133478035 -1.203472671
##  [61] -0.899762531 -1.006446958 -0.437812701  1.712300783 -1.263885916
##  [66] -1.604219653  4.488026052 -0.665172931 -1.668377900 -1.130422629
##  [71]  3.316812797  2.172380940  0.572326326 -1.827615023  0.720276568
##  [76]  0.849193077 -0.640547040 -0.095120639 -0.045215749 -1.769164273
##  [81]  0.718379560 -1.678008963 -0.895860760 -1.627068924 -1.331489281
##  [86]  0.909892498  2.680823986  1.353531002 -1.678967186 -2.304099591
##  [91]  0.741204117 -0.809147683 -0.790428226  1.549314451 -1.647991336
##  [96] -0.268121798 -0.103534223 -0.776307350  1.103113756 -0.409442426
## [101]  4.633190126 -0.740349810  0.704221402 -0.385204834 -0.068793640
## [106] -0.692576410  0.345220609 -1.364096376 -0.387521866  0.491580932
## [111] -1.087373932  1.210180885  1.869006469  0.492734252  0.889433533
## [116] -0.849321798  1.382626614 -0.876114257  0.129510618  0.006142764
## [121] -0.669636518  1.757579745  1.875711497  0.312604564 -0.681074580
## [126] -0.863182056 -0.118572831 -1.423953866 -1.441335172 -0.856545337
## [131] -1.307398005  0.585398503 -1.786207788 -1.427017695  0.756062138
## [136]  0.145449916 -0.274324587 -0.438129117  1.064299809  2.098096298
## [141] -1.849943605 -0.732556857 -0.608595125  0.505611656  0.247551976
## [146] -0.602802743 -1.272341157  2.651497970 -1.824221268 -0.352147008
## [151] -1.129437762 -0.549974224 -1.104925141 -1.260493668 -1.263788087
## [156]  2.182293451 -0.839030427 -1.567211240 -0.656681669  1.746317858
## [161]  0.576848393 -1.591129974 -1.734769097 -1.257058960  0.171012852
## [166]  0.763873736 -0.648233872  4.075761272  0.108096807 -1.498040609
## [171]  0.047885996  1.337596168 -1.358485537 -1.872027381 -1.311243234
## [176]  1.309706033 -0.190859319 -1.150520519  1.562083350  0.457663612
## [181] -1.138195339 -0.007740653 -1.442466409  1.401099127  3.044609211
## [186] -0.608848019  0.869481448 -0.300778748  0.636747830 -1.117892469
## [191] -0.433517740 -2.074508151 -0.943857160 -0.671437346  3.146400023
## [196] -1.646968799  0.194381857  1.355794604  0.342080981 -0.390007297
## [201] -0.278709707 -0.042662340 -1.773111892  1.250439359 -1.763032603
## [206] -1.734908122 -0.040455138 -0.686284826 -0.444359734  0.691490501
## [211]  2.007551495  2.980951104 -0.051043670 -1.433696923  0.663189426
## [216]  2.031410016  0.789603453  0.673484381 -1.540903396  4.811125983
## [221]  2.960210184  0.548555090 -1.203818787 -0.095903547 -1.447284264
## [226] -0.721456172  2.040310983  1.855207556 -1.362709085 -0.288896751
## [231] -0.418601999 -1.163850583  0.411132602 -1.693135796 -1.469262447
## [236] -1.241804213  3.689808324  0.637785394  6.741912903 -1.238593026
## [241]  0.823175506  0.046147404 -0.926653518  1.642861658  0.577872627
## [246] -1.754825326 -2.038325012  0.534102452 -0.778602587 -1.358620602
## [251]  0.552972231  0.160512695 -0.255760964  2.380048532  2.562080786
## [256] -0.556325503 -1.361977024 -1.604168388  0.453544197 -0.245088734
## [261] -0.586494355 -0.595783004 -0.098509308 -1.732739711 -1.312518153
## [266] -1.117483636 -0.802242010  1.779574174 -0.692885384 -0.296827034
## [271]  2.648459041 -0.009329958  0.636626889 -0.730329225  0.329127497
## [276] -1.859016837  2.011187895  4.387657320 -1.562200265  1.140064695
## [281] -1.592089421 -0.863852065  1.027169030 -0.436517354  0.337411799
## [286]  0.922063650  0.074518204  0.517903752  1.205633993  5.667322803
## [291]  0.117634314 -1.257776898 -1.442594978  0.581815447  3.192976367
## [296] -1.664428065 -1.381280799 -0.359580844 -1.295214100  1.275367360
## [301]  0.510190648  0.497692443 -0.360524908  0.680162177  0.651993920
## [306]  3.788964776  0.324102302  1.241627938 -0.511968929  0.718039754
## [311] -0.310163020 -1.033055205 -0.764852259  2.840965510 -1.178758036
## [316] -0.802177079  1.938258838 -1.084340607  5.007927517 -0.352175349
## [321] -1.645893870 -0.723629619  2.150497872  0.219479185 -0.347437994
## [326] -0.234908136  0.016559745 -1.467247701  1.154836707  0.020892606
## [331]  0.169022729  0.596241854 -1.658882001 -1.130296134 -0.114349001
## [336] -1.180178802  1.016962553  1.874901202 -1.674481841  0.347838749
## [341] -0.523787799 -1.191298001  1.808772263 -1.770065768 -0.206433118
## [346]  0.781356058 -1.821829245 -0.284787326 -0.436832085 -1.217940564
## [351]  1.408443279  0.076806137 -1.371613972 -1.864312777 -1.989259900
## [356] -0.666931670 -0.752021652 -0.799705965 -1.601727166 -1.657122757
## [361] -0.384493964 -1.117824446  2.156938592 -0.789754021 -1.380570918
## [366] -1.291560292 -0.935262338  2.492171120 -0.327363502 -1.468296601
## [371]  0.644477407  4.369563022 -2.357052820  0.718708019  1.391878059
## [376]  0.905097897  3.157230391  0.003135705 -0.242056357
#The aboved two gives us the same thing. predict is a good function to know.
Cancer$Survivor <- as.factor(Cancer$Survivor)
out <- sapply(1:5, function(i){plot(Cancer$Survivor,Cancer_pca$x[,i],xlab=paste("PC",i,sep=""),ylab="Survivor")})

# Factor Analysis
#EFA

library(psych)
## 
## Attaching package: 'psych'
## The following object is masked from 'package:car':
## 
##     logit
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
Cancer<- read.csv("~/Downloads/Cancer_Breast.csv")

attach(Cancer)
Cancer[1]
##     Survivor
## 1      Alive
## 2      Alive
## 3      Alive
## 4      Alive
## 5      Alive
## 6      Alive
## 7      Alive
## 8       Dead
## 9      Alive
## 10     Alive
## 11      Dead
## 12     Alive
## 13     Alive
## 14     Alive
## 15     Alive
## 16     Alive
## 17     Alive
## 18     Alive
## 19     Alive
## 20     Alive
## 21     Alive
## 22     Alive
## 23     Alive
## 24     Alive
## 25     Alive
## 26     Alive
## 27     Alive
## 28     Alive
## 29     Alive
## 30     Alive
## 31     Alive
## 32     Alive
## 33     Alive
## 34     Alive
## 35     Alive
## 36     Alive
## 37     Alive
## 38     Alive
## 39     Alive
## 40     Alive
## 41      Dead
## 42     Alive
## 43     Alive
## 44     Alive
## 45     Alive
## 46     Alive
## 47      Dead
## 48     Alive
## 49     Alive
## 50     Alive
## 51     Alive
## 52     Alive
## 53     Alive
## 54     Alive
## 55     Alive
## 56     Alive
## 57     Alive
## 58     Alive
## 59     Alive
## 60     Alive
## 61     Alive
## 62     Alive
## 63     Alive
## 64     Alive
## 65      Dead
## 66     Alive
## 67      Dead
## 68     Alive
## 69     Alive
## 70     Alive
## 71     Alive
## 72      Dead
## 73     Alive
## 74     Alive
## 75     Alive
## 76     Alive
## 77     Alive
## 78     Alive
## 79     Alive
## 80     Alive
## 81     Alive
## 82     Alive
## 83     Alive
## 84     Alive
## 85     Alive
## 86     Alive
## 87     Alive
## 88     Alive
## 89     Alive
## 90     Alive
## 91      Dead
## 92     Alive
## 93      Dead
## 94      Dead
## 95     Alive
## 96     Alive
## 97      Dead
## 98     Alive
## 99      Dead
## 100    Alive
## 101     Dead
## 102    Alive
## 103    Alive
## 104     Dead
## 105    Alive
## 106    Alive
## 107     Dead
## 108    Alive
## 109    Alive
## 110    Alive
## 111    Alive
## 112     Dead
## 113    Alive
## 114    Alive
## 115    Alive
## 116    Alive
## 117    Alive
## 118    Alive
## 119    Alive
## 120    Alive
## 121    Alive
## 122    Alive
## 123    Alive
## 124    Alive
## 125    Alive
## 126     Dead
## 127    Alive
## 128    Alive
## 129    Alive
## 130    Alive
## 131    Alive
## 132    Alive
## 133    Alive
## 134    Alive
## 135     Dead
## 136     Dead
## 137    Alive
## 138     Dead
## 139     Dead
## 140    Alive
## 141    Alive
## 142    Alive
## 143    Alive
## 144     Dead
## 145     Dead
## 146    Alive
## 147    Alive
## 148     Dead
## 149    Alive
## 150    Alive
## 151    Alive
## 152    Alive
## 153     Dead
## 154    Alive
## 155    Alive
## 156    Alive
## 157    Alive
## 158    Alive
## 159    Alive
## 160     Dead
## 161    Alive
## 162    Alive
## 163    Alive
## 164    Alive
## 165    Alive
## 166    Alive
## 167    Alive
## 168    Alive
## 169    Alive
## 170    Alive
## 171     Dead
## 172    Alive
## 173    Alive
## 174    Alive
## 175    Alive
## 176    Alive
## 177     Dead
## 178    Alive
## 179    Alive
## 180     Dead
## 181    Alive
## 182     Dead
## 183     Dead
## 184    Alive
## 185    Alive
## 186    Alive
## 187    Alive
## 188    Alive
## 189     Dead
## 190    Alive
## 191    Alive
## 192    Alive
## 193    Alive
## 194    Alive
## 195    Alive
## 196    Alive
## 197    Alive
## 198    Alive
## 199    Alive
## 200    Alive
## 201    Alive
## 202    Alive
## 203     Dead
## 204     Dead
## 205    Alive
## 206    Alive
## 207    Alive
## 208    Alive
## 209    Alive
## 210    Alive
## 211    Alive
## 212     Dead
## 213    Alive
## 214    Alive
## 215    Alive
## 216     Dead
## 217     Dead
## 218    Alive
## 219    Alive
## 220     Dead
## 221     Dead
## 222     Dead
## 223    Alive
## 224    Alive
## 225    Alive
## 226    Alive
## 227    Alive
## 228    Alive
## 229    Alive
## 230    Alive
## 231    Alive
## 232    Alive
## 233    Alive
## 234    Alive
## 235    Alive
## 236    Alive
## 237    Alive
## 238    Alive
## 239     Dead
## 240    Alive
## 241     Dead
## 242    Alive
## 243    Alive
## 244    Alive
## 245    Alive
## 246    Alive
## 247    Alive
## 248     Dead
## 249    Alive
## 250    Alive
## 251    Alive
## 252    Alive
## 253    Alive
## 254    Alive
## 255    Alive
## 256    Alive
## 257    Alive
## 258    Alive
## 259    Alive
## 260    Alive
## 261    Alive
## 262    Alive
## 263    Alive
## 264     Dead
## 265    Alive
## 266    Alive
## 267    Alive
## 268    Alive
## 269     Dead
## 270    Alive
## 271     Dead
## 272    Alive
## 273    Alive
## 274    Alive
## 275    Alive
## 276    Alive
## 277    Alive
## 278     Dead
## 279    Alive
## 280    Alive
## 281    Alive
## 282    Alive
## 283     Dead
## 284    Alive
## 285    Alive
## 286     Dead
## 287    Alive
## 288    Alive
## 289    Alive
## 290     Dead
## 291    Alive
## 292    Alive
## 293     Dead
## 294    Alive
## 295    Alive
## 296    Alive
## 297    Alive
## 298    Alive
## 299    Alive
## 300    Alive
## 301    Alive
## 302    Alive
## 303    Alive
## 304    Alive
## 305    Alive
## 306     Dead
## 307    Alive
## 308    Alive
## 309    Alive
## 310    Alive
## 311    Alive
## 312    Alive
## 313    Alive
## 314     Dead
## 315    Alive
## 316    Alive
## 317    Alive
## 318    Alive
## 319    Alive
## 320    Alive
## 321    Alive
## 322    Alive
## 323    Alive
## 324    Alive
## 325    Alive
## 326    Alive
## 327    Alive
## 328    Alive
## 329    Alive
## 330    Alive
## 331    Alive
## 332     Dead
## 333    Alive
## 334    Alive
## 335    Alive
## 336    Alive
## 337    Alive
## 338    Alive
## 339    Alive
## 340    Alive
## 341    Alive
## 342    Alive
## 343    Alive
## 344    Alive
## 345    Alive
## 346    Alive
## 347    Alive
## 348    Alive
## 349    Alive
## 350    Alive
## 351    Alive
## 352    Alive
## 353    Alive
## 354    Alive
## 355    Alive
## 356    Alive
## 357    Alive
## 358     Dead
## 359    Alive
## 360    Alive
## 361    Alive
## 362    Alive
## 363     Dead
## 364     Dead
## 365    Alive
## 366    Alive
## 367    Alive
## 368    Alive
## 369    Alive
## 370     Dead
## 371    Alive
## 372     Dead
## 373    Alive
## 374    Alive
## 375    Alive
## 376    Alive
## 377    Alive
## 378    Alive
## 379    Alive
fit.pc <- principal(Cancer[-1], nfactors=5, rotate="varimax")
fit.pc
## Principal Components Analysis
## Call: principal(r = Cancer[-1], nfactors = 5, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                          RC1   RC2   RC5   RC4   RC3   h2      u2 com
## Age                    -0.11 -0.03  0.01  0.99  0.01 1.00 0.00067 1.0
## Stage                   0.94  0.07  0.00 -0.07 -0.03 0.89 0.10629 1.0
## Tumor.Size              0.93  0.12 -0.09 -0.07  0.00 0.89 0.10621 1.1
## Regional.Node.Examined -0.05  0.91  0.06  0.01 -0.06 0.83 0.16842 1.0
## Reginol.Node.Positive   0.37  0.73 -0.17 -0.07  0.04 0.70 0.29643 1.6
## Survival.Months        -0.06 -0.04  0.99  0.01  0.06 0.99 0.01323 1.0
## Sex                    -0.02 -0.03  0.06  0.01  1.00 1.00 0.00318 1.0
## 
##                        RC1  RC2  RC5  RC4  RC3
## SS loadings           1.90 1.38 1.02 1.00 1.00
## Proportion Var        0.27 0.20 0.15 0.14 0.14
## Cumulative Var        0.27 0.47 0.61 0.76 0.90
## Proportion Explained  0.30 0.22 0.16 0.16 0.16
## Cumulative Proportion 0.30 0.52 0.68 0.84 1.00
## 
## Mean item complexity =  1.1
## Test of the hypothesis that 5 components are sufficient.
## 
## The root mean square of the residuals (RMSR) is  0.06 
##  with the empirical chi square  58.1  with prob <  NA 
## 
## Fit based upon off diagonal values = 0.94
round(fit.pc$values, 3)
## [1] 2.245 1.178 1.061 0.941 0.881 0.507 0.187
#Infernce
# In the round function we can infer that there are six eigenvalues displayed in descending order.

fit.pc$loadings
## 
## Loadings:
##                        RC1    RC2    RC5    RC4    RC3   
## Age                    -0.106                0.993       
## Stage                   0.939                            
## Tumor.Size              0.931  0.118                     
## Regional.Node.Examined         0.906                     
## Reginol.Node.Positive   0.370  0.730 -0.167              
## Survival.Months                       0.989              
## Sex                                                 0.996
## 
##                  RC1   RC2   RC5   RC4   RC3
## SS loadings    1.904 1.377 1.021 1.002 1.002
## Proportion Var 0.272 0.197 0.146 0.143 0.143
## Cumulative Var 0.272 0.469 0.615 0.758 0.901
# Loadings with more digits
for (i in c(1,3,2,4)) { print(fit.pc$loadings[[1,i]])}
## [1] -0.1063485
## [1] 0.007309789
## [1] -0.03169656
## [1] 0.9933908
# Communalities
fit.pc$communality
##                    Age                  Stage             Tumor.Size 
##              0.9993287              0.8937139              0.8937913 
## Regional.Node.Examined  Reginol.Node.Positive        Survival.Months 
##              0.8315783              0.7035652              0.9867685 
##                    Sex 
##              0.9968239
## The output shows the communality values for each variable in the dataset. The values range from 0 to 1, with higher values indicating that a greater proportion of the variance.
## The variable "Age" has a communality value of 0.9993287, indicating that almost all of the variance in age can be explained by the other variables in the model. Similarly, the variables "Stage", "Tumor.Size", and "Survival.Months" all have high communality values.
## On the other hand, the variables "Regional.Node.Examined" and "Reginol.Node.Positive" have lower communality values.

# Rotated factor scores, Notice the columns ordering: RC1, RC3, RC2 and RC4
fit.pc$scores
##                 RC1          RC2           RC5          RC4        RC3
##   [1,] -1.307322343  0.720541453 -0.4109466207  1.432199590 -0.5995915
##   [2,]  0.125258717 -0.005991665 -0.3960011664 -0.446560393 -0.5032814
##   [3,]  1.521528245  0.036535290  0.2675298647  0.576373054 -0.5207671
##   [4,] -0.576956591 -1.270969616  0.3457891320  0.284757521 -0.5355061
##   [5,]  0.356003626 -1.429130282 -1.0038777695 -0.793721798 -0.4937427
##   [6,] -0.898825264  0.255382282  0.7824421029 -0.435014544 -0.5902173
##   [7,] -1.123345808 -0.495508261 -0.8492879225 -0.480027023 -0.5198397
##   [8,] -0.166918910 -0.929718498 -2.5074915609 -1.569559540 -0.4551006
##   [9,]  2.895698210  1.407000989  0.0701621060 -1.232915129 -0.3627589
##  [10,]  1.623286547  1.166469031  1.1339661602  1.804724621 -0.5607949
##  [11,] -0.796737103 -0.643134432 -0.4467304353  1.405298813 -0.5386135
##  [12,]  1.383407566 -0.613812751  1.0606014044 -0.771008966 -0.5964824
##  [13,]  0.231378332 -0.277381746 -0.6480718231  1.212891868 -0.5306287
##  [14,] -1.209097244  1.129275448 -1.4960382009 -0.757923760 -0.4399465
##  [15,]  0.332062691  1.089576672 -0.4600933919  0.880089204 -0.3798997
##  [16,] -1.005709045  0.294230470 -0.9459212280  0.683789562 -0.5499190
##  [17,]  0.744674990 -1.521478193  1.3942774551  0.198005816 -0.5882018
##  [18,] -0.392840627  0.331740014 -0.2023918755 -1.219299086 -0.6020107
##  [19,] -0.070089438 -0.131860914  1.6981587841 -0.691186435 -0.6608646
##  [20,] -0.051436133  0.191789657  0.4212599841  0.665104459 -0.6298133
##  [21,] -0.006732381 -0.175158552  0.5162044500 -0.678069438 -0.5910345
##  [22,]  0.235767119  0.064736618 -0.9160969551  0.345887419 -0.4880382
##  [23,]  0.238416634 -1.252012775  0.2398637050  0.059950918 -0.5605271
##  [24,]  1.485603522 -0.192706771  1.6426949223 -0.500072971 -0.6715799
##  [25,] -0.638645746  2.989208025  0.9036488179  0.790027137 -0.3283707
##  [26,] -0.178437490  2.777908908 -0.0413468810  1.003449656 -0.4138383
##  [27,]  0.582909298  2.785940166  1.1903597199 -0.617407633 -0.3249590
##  [28,] -0.958925042 -0.214668978  0.4376328731 -1.006550454 -0.5747757
##  [29,] -0.030712394 -0.064531047 -0.2958902002  0.303786095 -0.5331017
##  [30,]  0.068379476 -0.661628273  0.6696875518  1.275338778 -0.6122729
##  [31,]  0.341019051 -1.423515415 -0.9156870304 -0.796564772 -0.4978896
##  [32,] -0.849797464 -1.056311111 -1.1560432828 -0.259833717 -0.4831038
##  [33,] -0.695855576 -0.893221994  0.6669447747  0.399805322 -0.5655454
##  [34,] -0.904371285  0.418390526 -0.4227821023  0.568333687 -0.5359795
##  [35,] -0.134717535  0.896879252 -1.7893854324 -0.883820975 -0.3884290
##  [36,] -0.962782744 -0.496271026  0.0146280532 -0.506395204  1.8698186
##  [37,] -0.216070538  0.760054595 -1.5310060164 -0.017108670  1.9268830
##  [38,] -0.822162376 -0.027741225  1.2379223356 -0.475255516  1.8060242
##  [39,]  0.207377292 -0.584119832  0.3835243419 -0.591160486  1.8359579
##  [40,] -0.015945155  0.231547364  1.4102652463 -0.390085871  1.8134154
##  [41,]  1.672295634  0.331889914 -1.4195501472  0.458760335  2.0373001
##  [42,] -0.810396953 -0.246830664 -0.6575095163  0.962169014  1.8807243
##  [43,]  0.192702901 -1.337412693  0.4521697808  0.787065016  1.8300087
##  [44,] -0.045240073  0.301893642  0.4610586322 -0.165708418  1.8659211
##  [45,] -1.114592031 -0.318549810 -0.5798944449 -0.067077011  1.8811846
##  [46,]  1.433075757 -0.404070935  0.7973567945  1.398145800  1.8307848
##  [47,] -1.300369551 -0.028825995 -1.5735162921 -1.478447862  1.9188192
##  [48,] -0.890968449 -0.347396610 -0.7258310349  0.737085989  1.8686802
##  [49,]  0.161477066  0.663117873  0.3316500047 -0.142306077  1.9180601
##  [50,] -0.856746942 -0.435474034  0.1880548609  1.468182616  1.8657762
##  [51,] -0.312541977  0.136516082 -0.0161195165 -1.924986682  1.8441573
##  [52,]  1.447543637 -0.924569775  0.0183976951  1.743586990  1.8054576
##  [53,]  2.812048369 -1.262055827  0.6755524008  0.899216739  1.8278901
##  [54,]  1.638406126  0.094433947  0.1223316011  1.168921857  1.7927188
##  [55,] -1.245588504  0.059259832 -0.0048643311  0.161759900  1.8212159
##  [56,] -1.016071990 -0.238010351 -0.0883995005 -0.046799422  1.8419097
##  [57,] -0.055136450  0.137116743  1.0235735974  0.870721586 -0.6544031
##  [58,] -1.556238684  2.969335661  1.9976509472 -0.452852539 -0.7682586
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## [112,]  1.263393891 -1.347298151  0.3756429440 -1.810192301 -0.5372158
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## [116,] -0.872120563 -0.235055775 -0.9604664732 -0.229531597 -0.4840017
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## [121,]  0.470777695 -0.853494484  0.9640285036  1.408655642 -0.5912659
## [122,]  1.405049166 -0.336954364  0.6651494977 -1.074659082 -0.6360513
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## [124,]  0.137527966  0.747763928  0.8076285109  0.582272820 -0.6052919
## [125,] -1.207472037  0.659121375 -0.9173575548 -0.202538944 -0.5431849
## [126,] -1.059365232 -0.111863156 -2.5520963763  0.783045168 -0.4715829
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## [128,] -0.668485812 -1.234189812 -1.1437986452  0.407393990 -0.4784974
## [129,] -0.781412414 -0.636562877  0.1921706334  0.075484452 -0.5360648
## [130,] -0.910852125 -0.118141856  0.1648322582 -1.118686080 -0.5283327
## [131,] -1.054611407 -0.224369817 -0.9889128447  0.533778669 -0.5299576
## [132,]  0.464743589 -0.274594110  0.0164014242 -0.437583960 -0.4849109
## [133,] -0.791113077 -0.698514147  0.9608865271  0.287071463 -0.5857403
## [134,] -0.659497302 -1.015874150  0.5276646413 -0.586459449 -0.5469555
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## [137,] -0.073092241 -0.529798193  0.6252597940 -0.921182815 -0.6010368
## [138,] -0.203813683  0.205421901 -0.0264975808  1.200467588 -0.6195221
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## [140,]  1.647651857  0.610335052  1.5748732495 -0.064357662 -0.5501517
## [141,] -0.877936142 -1.067222622  0.4630349522 -0.179017558 -0.5506706
## [142,] -0.880884628  0.001296777  1.2578449106 -2.117603851 -0.5506924
## [143,] -1.234037531  0.639326115 -0.8362718207 -0.636374887 -0.5613370
## [144,]  0.018914773  0.586259602 -1.1209844572  0.923196157 -0.5439073
## [145,] -0.074225213  0.130334822 -0.6786655391  0.018113001 -0.5778125
## [146,]  0.170669790 -0.211946375  1.6757272129  0.756563815 -0.6630197
## [147,] -1.268831196  0.292072878  0.9147393097 -1.028463825 -0.6007164
## [148,]  1.499625720 -0.046845209 -0.7664088417 -1.614411093 -0.4402786
## [149,] -0.529536340 -1.369987365 -0.3375678645  1.169593364 -0.5097680
## [150,]  0.045962946 -0.222375155  0.5034601041  0.519382186 -0.5787514
## [151,] -1.223856305  0.180228884  1.3388657689 -1.902230693 -0.6246961
## [152,] -0.055594722 -0.235365155 -0.2657174148  1.402153010 -0.5741668
## [153,] -0.872397774 -0.149800492 -0.7512698901  0.558351518 -0.5383938
## [154,] -0.759782685  0.237400082  1.0571700070  0.642200810 -0.5512758
## [155,] -0.813251671 -0.121758378 -0.7460735201  1.323805143 -0.5259434
## [156,]  2.383554586  0.066385562  1.0240913311  1.889523847 -0.5619446
## [157,] -1.062479680 -0.170739143 -0.9195452905 -0.886941417 -0.5237196
## [158,] -1.005317425 -0.888953898  1.2099661543 -1.835444628 -0.5775630
## [159,]  0.136829559 -1.433075986 -0.0981173560 -0.178909817 -0.5407191
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## [162,] -0.963767612 -1.209402888 -1.0097948507 -0.286821264 -0.4861585
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## [173,] -0.912245486 -0.543537627  0.4318793073 -0.704266778 -0.5460481
## [174,] -0.856725188 -0.606275067  0.5729083794  0.837849047 -0.5788037
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## [177,] -0.852527763  0.913073674 -1.2487037530  0.443288986 -0.3889680
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## [179,] -0.303095538  2.430866190 -0.6384654771 -0.201183782 -0.4254171
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## [181,] -1.321017616  1.460485536  1.1701106295  0.581488250 -0.6841998
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## [183,] -0.838250697 -1.253469930 -2.3420645082  0.840178824 -0.4357410
## [184,]  0.305952116  0.857628124 -0.6208265049 -0.658481536 -0.3719988
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## [186,]  0.084230885 -0.213495242  0.7088044114  1.297328954 -0.6110553
## [187,]  1.900171708 -1.333994230  0.4460048652  1.662025940 -0.5533245
## [188,] -0.031255932 -0.250326762  0.0512696801  0.414798230 -0.5783953
## [189,] -0.289943685  2.280655792  1.0403578757  0.907822811 -0.5892244
## [190,] -1.009608297 -0.214185385  0.3044822299 -1.010945193 -0.5704291
## [191,] -0.100171533 -0.538302371 -0.4453568020  0.403768412 -0.5676653
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## [194,]  0.113174094 -1.143735733  0.5197044925 -0.171621885 -0.5768705
## [195,]  1.619999756  0.722080241 -0.6887746694 -1.159310467 -0.3796617
## [196,] -0.841575560 -1.027342691 -1.1199979302  0.836707596 -0.4940180
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## [198,]  1.508468375 -0.491771290  1.2706156675 -0.331862633 -0.5733863
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## [202,] -0.048425605  0.118699074 -0.3136137325  0.642414413 -0.5418371
## [203,] -0.725973475 -1.391564031 -1.4003029111  1.159176023 -0.4696420
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## [205,] -0.591881423 -1.282634627 -0.3662711589  0.949207996 -0.5113297
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## [209,] -0.007891195 -0.524824404  0.2643233157  0.186914850 -0.5935579
## [210,]  1.315655920 -1.271003485  1.2303045822 -0.591116393 -0.6691135
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## [212,]  0.940649088  0.701231310 -2.4261194871 -1.758097235 -0.3364648
## [213,] -0.843475892  1.798200749  1.2431300083 -0.367011334 -0.3878258
## [214,] -0.781235959 -0.674221447 -0.7959006505  0.863359707 -0.5185426
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## [216,]  2.013102794 -1.296736506 -2.4252777270  1.165171752 -0.4116134
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## [219,] -0.615077289 -1.015667708 -0.6218595627  0.958425491 -0.4924325
## [220,]  1.579631766  3.062368813 -2.2203707613 -0.244083273 -0.1502356
## [221,]  1.622510136  0.524966677 -2.0982929217  0.271136908 -0.3258956
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## [223,] -1.057220701  0.294743996  1.5799985058 -1.011438246 -0.6235200
## [224,] -0.072963987 -0.613282713  0.1918476357 -1.267968895 -0.5409381
## [225,] -0.743196363 -1.287157686  0.4887299593 -1.380676965 -0.5315434
## [226,] -1.204399934  1.078327729  1.4467583839 -1.303364197 -0.6464837
## [227,]  1.266507000  0.767534233 -0.3503472066  0.692688427 -0.4909861
## [228,]  0.526231893  1.970061816  0.3846572483  0.309208920 -0.7235692
## [229,] -0.807888294 -0.682277954 -0.9271201774  0.642588683 -0.5117319
## [230,]  0.260702126  0.067500856  0.9960447880  1.314943629 -0.5922170
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## [232,] -0.748149400 -0.235684355 -0.8098530912  1.057905702 -0.4242444
## [233,]  0.221132345  0.726284680 -0.4706900842  1.694958562 -0.5404234
## [234,] -0.678124359 -1.286173092 -0.3631724375  0.390948883 -0.5089168
## [235,] -0.777964457  0.022014698  0.9511963866  0.874901501 -0.5965360
## [236,] -1.104199886  0.893106757  0.1508009585  1.461183918 -0.6243581
## [237,]  1.267361233  2.458544324 -0.7953591503 -0.506357472 -0.3026893
## [238,]  1.414804958 -0.669338141  1.5879145612  0.881868537 -0.6651199
## [239,]  3.072830030  2.797446004 -2.3543948743 -0.829644350 -0.1642152
## [240,] -0.977591464 -0.650161151  0.1113674239 -1.261989255 -0.5262341
## [241,] -0.227173805  0.909077465 -0.6761278347 -0.714541067 -0.6028713
## [242,] -0.374860641  1.224103876  1.5224233299 -0.207629831 -0.6934552
## [243,]  0.339285030 -0.632685804  1.5643586931  1.616720947 -0.6283326
## [244,]  0.193419437  1.349621084  0.3181259367 -1.657692381 -0.3859751
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## [246,] -0.986864785  0.228162453  1.4086212636  0.974617586 -0.6464221
## [247,] -0.824333365 -0.584737531  0.9684755951  1.165701465 -0.5976809
## [248,] -0.243577912  0.130329136 -1.2713044519 -0.998576041 -0.5126775
## [249,] -1.098189969 -0.042322071  0.2618826295 -2.004312474 -0.5506002
## [250,] -0.831659221 -0.461798444  0.8339709447 -0.575432129 -0.5829435
## [251,]  0.660868636 -0.613089041  1.4267428400 -1.550837320 -0.5179548
## [252,]  0.517181302 -1.252585113 -0.8002149569 -0.217372976 -0.5091529
## [253,]  0.212098480 -1.348423379  0.5118783711 -1.495414863 -0.5384487
## [254,]  1.382850183 -0.219189695  0.0269815816 -2.289775167 -0.5008942
## [255,]  2.316252786 -0.154520000 -0.6196502617  1.491962124 -0.5581641
## [256,] -0.052222397  0.342831758  1.1030769253  1.421123613 -0.6508161
## [257,] -0.947651993 -0.182837344  0.1296818993  0.195421008 -0.5540779
## [258,] -0.817512860 -0.840561713 -0.7371019278  0.846637304 -0.5158444
## [259,]  0.024440224  0.135810865  0.5253487099 -1.299969431 -0.6149952
## [260,]  0.067041636 -0.555778718 -0.3100055514  0.312345291 -0.5681031
## [261,] -1.306437681 -0.486601364 -2.9400342325 -1.465663796 -0.4121852
## [262,] -0.014493236 -0.760844445  1.4659197736 -0.941980042 -0.6260813
## [263,]  0.087915119 -0.726396470  0.1214379164 -0.806812211 -0.5523444
## [264,] -0.663255841 -0.978208815 -0.4379015412  1.270596257 -0.4865597
## [265,] -1.264717983  1.570034295  1.4005006577  1.358429987 -0.7023310
## [266,]  0.329489028 -1.280600310  1.1901799282  1.149389977 -0.6051367
## [267,] -1.275441818  1.489909511 -0.3653351658  1.159328260 -0.6254954
## [268,]  1.467219795 -1.417456695 -0.4139644655 -2.214884058 -0.4944306
## [269,]  0.074431066 -1.269331784 -1.2275551559  1.044679444 -0.5109551
## [270,] -0.870383997  1.198615078 -1.1667852458  1.224951761 -0.4088626
## [271,]  1.192803950  0.057498971 -1.3162984144 -2.085355644 -0.4062685
## [272,] -0.286304144  0.269404319 -0.4804269869  0.097343658 -0.5779838
## [273,] -0.073564499  0.119038694 -1.1825747303 -0.760302162 -0.5139350
## [274,] -0.625006769  0.138379186 -0.0610686387  0.302269025 -0.4228122
## [275,] -0.021173080 -0.700817241 -0.6634415846 -1.782093243 -0.5340527
## [276,] -0.884025238 -1.266723243 -0.3639584298  0.147357974 -0.5123415
## [277,]  2.516442608 -1.491783291 -0.9242054613  1.431531304 -0.4938464
## [278,]  2.031372112  1.640945832 -2.3907351702  0.035674946 -0.2684863
## [279,] -0.644202099 -0.060835451  1.1558321022  1.320821549 -0.6025201
## [280,]  1.365402375 -0.326500585  0.9183043363  0.451750843 -0.6106705
## [281,] -0.998554369  0.016290020  0.6748709397  0.641599115 -0.6064536
## [282,] -0.976425065 -0.330623146 -0.5822879576 -1.120432404 -0.5099230
## [283,] -0.174096618  0.831315104 -1.6751635447 -0.457324464 -0.3950843
## [284,] -0.082408280 -0.401303006  0.9559754038 -0.490726480 -0.6044327
## [285,]  0.324609780 -0.319056104 -0.2055106283 -0.087924887 -0.5533704
## [286,]  0.518974388 -0.626556061 -2.2391579236  0.016972147 -0.3820568
## [287,]  0.136338831 -0.397804971 -0.8891820787  0.440183790 -0.5308955
## [288,]  0.506305649  0.481023442  1.4465880168  0.205153662 -0.4827936
## [289,] -0.679085140  3.954507874  0.5752992943  1.453201950 -0.2448900
## [290,]  2.470404344  2.991945738 -0.5290849496 -1.029346539 -0.4106261
## [291,] -0.475228178  1.932813957  1.3550208886  0.824447532 -0.7400227
## [292,] -0.893427799  0.052715870 -0.4613924173  1.112064914 -0.5622336
## [293,] -0.766179776 -0.496035153 -1.0366271901  1.537370973 -0.5198040
## [294,]  0.051327695  0.583240262  1.1204588327 -1.214434393 -0.5636789
## [295,]  2.307456533  0.621920510  1.2403951582 -0.573363752 -0.4752943
## [296,] -0.823373549 -0.553530401 -0.3874675192  1.297680786 -0.5439481
## [297,] -0.638856713 -1.392890187  0.2086421620 -1.151578219 -0.5157354
## [298,]  0.236428819 -0.304190499  0.4080938392  1.186158238 -0.5545552
## [299,] -1.158398890  0.459133650  0.9733411651 -0.228477624 -0.6310363
## [300,]  1.475928783 -0.465493278 -0.6496321968  1.573970535 -0.5475340
## [301,]  0.319282803 -0.049075834  1.0290757671 -1.173237425 -0.6235565
## [302,] -0.296881139  0.494890288 -0.7837240475 -0.759473987 -0.5668933
## [303,] -1.346283968  1.396610113 -0.3020330196 -0.736283603 -0.5749707
## [304,] -1.348923740  3.967904918  0.2810558784  0.853221032 -0.5000464
## [305,]  0.162334597  0.973501593 -0.8686897807  1.600774950 -0.5332751
## [306,]  2.928736792 -0.255787116 -1.5103405908  0.623105829 -0.3507467
## [307,] -0.413597465  0.552421592  0.3355218007 -1.562746957 -0.5930447
## [308,]  1.237268932 -0.620592731 -0.5297194107  0.318227418 -0.5243271
## [309,]  0.241534706 -1.255128355  0.3749229830 -0.270115000 -0.5633189
## [310,] -0.115056477  0.218246789 -0.5441551566 -1.534291346 -0.5385641
## [311,]  0.244949439 -1.172546026  0.0029643917 -0.377648048 -0.5316625
## [312,] -0.881231270  0.271009722 -0.9229121503  1.315229206 -0.4789581
## [313,] -0.895696902  0.278400309 -0.2835395432 -0.127721411 -0.4762479
## [314,]  1.378787835  2.228549730  1.1028844251  0.377888253 -0.4504376
## [315,] -0.819270215 -0.389229359  0.6735990662 -0.785367895 -0.5769465
## [316,]  0.112830419 -1.229214807  0.2809164140  0.263772463 -0.5674737
## [317,]  1.653170530 -0.638926558 -0.1359545091 -0.591715251 -0.5782033
## [318,] -0.923159566 -0.009789760  0.0392931644 -0.126366446 -0.5350174
## [319,]  2.041830205  2.728680897 -0.6132687405 -1.177952321 -0.2601160
## [320,]  0.108549504 -0.557326273 -0.7579426821  1.199487472 -0.5556193
## [321,] -1.058133104  0.221889100  1.4569044176  0.307985872 -0.6445830
## [322,] -1.166517392 -0.171968667 -0.6482591292 -1.888956078 -0.5293544
## [323,]  1.727577762 -0.994955045 -0.2537868427 -1.608687974 -0.5146231
## [324,]  0.119079205  0.714209952  0.8669879471  0.657028497 -0.5526573
## [325,] -0.081826498 -0.166801362  0.1875315695  0.421707145 -0.6064362
## [326,]  0.099920940  0.282483183  1.0020969210  0.961338975 -0.5642588
## [327,]  0.243378159 -0.044682951  1.2128958236 -0.120393721 -0.5863570
## [328,] -0.844568806 -1.386731019 -0.1014289418 -1.391403864 -0.5059844
## [329,]  1.888859941 -1.054748117  1.0499863677  0.811763660 -0.6672029
## [330,]  0.228124222  0.115515456  0.6542582753  0.614143857 -0.4835419
## [331,] -0.056327449  0.548577051  1.5064192570 -0.749987819 -0.6759784
## [332,] -0.323716119  0.089322447 -2.3012144370 -0.658113240 -0.4916334
## [333,] -0.573599036 -0.673945940  1.3808133533  0.399976500 -0.5632159
## [334,] -1.050907273  0.238225132 -0.0290456556  0.113480081 -0.5822721
## [335,]  0.067385310 -0.470299644 -0.0712174729 -0.123049056 -0.5774999
## [336,] -0.908718064 -0.377913492  0.3293332486 -0.800496172 -0.5467791
## [337,]  1.498468230 -1.471211322 -0.1108668839 -0.120909521 -0.5573615
## [338,]  2.034240811 -0.624734880 -0.0001672349  0.977509078 -0.5696230
## [339,] -0.941394422  0.554847796  1.0125561096  1.183788414  1.7975113
## [340,]  0.116552431 -0.162234038 -0.5812925108 -1.016758341  1.8988221
## [341,] -0.073108062 -0.258456641  0.5642638902 -0.288911824  1.8266773
## [342,] -1.095299260  1.140502682 -0.0782396875  1.271318757  1.9275930
## [343,]  1.302176223 -0.312844591 -0.3730818043 -1.400463413  1.8215573
## [344,] -0.998956914 -0.576689506  0.4762144801 -0.623029529  1.8354088
## [345,] -0.166864133  0.930549169  0.1879962742  1.188073661  1.8234945
## [346,]  0.444933776  0.569084471 -0.2248211922  0.085279123  2.0038440
## [347,] -0.793884694 -0.930738805  1.0855863176 -0.958327240  1.8299915
## [348,]  0.076643584 -0.008551844  1.3088948879 -0.582715582  1.7746895
## [349,] -1.384810454  1.995909568 -0.2337161697 -0.236952360  1.9093380
## [350,] -0.934572665  0.209784179  0.2624276064 -0.240002684  1.8334865
## [351,]  0.994896423  0.734903211  1.6522061698 -0.990509561  1.7462317
## [352,]  0.011956605  0.139481088 -0.5020461494 -0.026141451  1.8748573
## [353,] -0.938648886 -0.930231873 -1.6000667152 -0.498723797  1.9336654
## [354,] -0.975524130 -0.740678639  1.0250360445 -1.077007603  1.8226366
## [355,] -0.723077419 -1.282766287  1.1606939574 -0.974269193  1.8409410
## [356,] -0.171118857  0.065130684 -0.6052809737  1.508045589  1.8105869
## [357,] -1.105820530  0.706046414 -0.5775661326 -0.543795765  1.8492150
## [358,]  0.199909474 -1.022116250 -0.9413885677  1.367514283  1.8902877
## [359,] -0.766697782 -1.157875422 -0.0920143761 -0.952566415  1.8869981
## [360,] -0.935248613  0.416620219  0.4014957360  1.422645689  1.7891634
## [361,] -0.034142609 -0.592841094 -0.9056044060  0.053421438  1.8787911
## [362,] -1.020311568  0.667748213  1.3451742682 -0.882893500  1.7576795
## [363,]  1.503081995  0.497724205 -0.8508028245  0.418045118  1.8398103
## [364,]  0.339567925 -1.258668199  1.0621879893 -0.411355661  1.8331884
## [365,] -0.878881317 -0.303149718  1.3785128159 -1.597249351  1.8173742
## [366,] -0.738203710  0.326579074 -0.1093419712  1.310637661  1.8736257
## [367,] -0.844541325  0.913100228  0.6777806934  0.311159619  1.8810449
## [368,]  2.206718168  1.120359115  1.0545424190  1.675635597  1.8372605
## [369,]  0.478510000  0.020594005  1.4993742541  0.979616572  1.7993268
## [370,] -0.655552750  0.197720065  0.3232111057  1.505296670  1.8972806
## [371,] -0.170573823  2.157417514  0.7973523682  0.546617198  1.8702915
## [372,]  3.055471856  0.696475884  0.0263444609 -0.807508660  1.9940047
## [373,] -0.592689309 -1.166518230  1.0294289591  1.021432409  1.8295919
## [374,] -0.096223023  0.811249314 -0.9120283373 -0.644753711  1.8706498
## [375,] -0.345022305  1.918486831 -0.6107381920 -1.678122770  1.9867217
## [376,]  0.576369263  0.862717139  0.5818314310  0.099965846  1.9815445
## [377,]  2.198335581  0.451180405 -0.7156699293 -0.242911092  2.0216293
## [378,] -0.190824950  0.066575923  0.5876761560 -1.704525215  1.8227795
## [379,] -0.066038449  0.053964866  0.6929418915 -0.577618988  1.7762757
# Play with FA utilities

fa.parallel(Cancer[-1]) # See factor recommendation

## Parallel analysis suggests that the number of factors =  2  and the number of components =  1
# Inference
# fa.parallel(Cancer[-1]) is performing a parallel analysis on the Cancer data set, excluding the Survivor variable. In a resulting scree plot we can compare the eigenvalues of the original data set to the mean and percentile values of the eigenvalues of the simulated data sets. The point at which the eigenvalues of the original data set intersect the mean or percentile values of the eigenvalues of the simulated data sets is a suggestion for the number of factors to retain.


fa.plot(fit.pc) # See Correlations within Factors

fa.diagram(fit.pc) # Visualize the relationship

vss(Cancer[-1]) # See Factor recommendations for a simple structure

## 
## Very Simple Structure
## Call: vss(x = Cancer[-1])
## VSS complexity 1 achieves a maximimum of 0.74  with  4  factors
## VSS complexity 2 achieves a maximimum of 0.81  with  4  factors
## 
## The Velicer MAP achieves a minimum of 0.07  with  1  factors 
## BIC achieves a minimum of  -36.66  with  2  factors
## Sample Size adjusted BIC achieves a minimum of  -11.28  with  2  factors
## 
## Statistics by number of factors 
##   vss1 vss2   map dof   chisq    prob sqresid  fit RMSEA BIC SABIC complex
## 1 0.49 0.00 0.072  14 9.4e+01 7.6e-14     4.8 0.49 0.123  11  55.0     1.0
## 2 0.54 0.61 0.079   8 1.1e+01 2.1e-01     3.7 0.61 0.031 -37 -11.3     1.3
## 3 0.64 0.73 0.144   3 2.2e+00 5.3e-01     2.4 0.74 0.000 -16  -6.1     1.3
## 4 0.74 0.81 0.272  -1 8.9e-02      NA     1.7 0.82    NA  NA    NA     1.1
## 5 0.62 0.66 0.555  -4 1.6e-09      NA     2.5 0.74    NA  NA    NA     1.4
## 6 0.60 0.68 1.000  -6 1.6e-12      NA     2.6 0.73    NA  NA    NA     1.4
## 7 0.60 0.68    NA  -7 1.6e-12      NA     2.6 0.73    NA  NA    NA     1.4
##    eChisq    SRMR eCRMS eBIC
## 1 1.1e+02 8.3e-02 0.102   26
## 2 1.2e+01 2.7e-02 0.044  -36
## 3 1.5e+00 9.8e-03 0.026  -16
## 4 1.0e-01 2.5e-03    NA   NA
## 5 5.8e-10 1.9e-07    NA   NA
## 6 5.1e-13 5.7e-09    NA   NA
## 7 5.1e-13 5.7e-09    NA   NA
# Computing Correlation Matrix
corrm.emp <- cor(Cancer[-1])
corrm.emp
##                                Age       Stage  Tumor.Size
## Age                     1.00000000 -0.17789979 -0.17541686
## Stage                  -0.17789979  1.00000000  0.80790600
## Tumor.Size             -0.17541686  0.80790600  1.00000000
## Regional.Node.Examined -0.02396398  0.07501922  0.09516337
## Reginol.Node.Positive  -0.11813829  0.34012221  0.39022509
## Survival.Months         0.02531278 -0.08063557 -0.15100312
## Sex                     0.02509020 -0.04136117 -0.02522026
##                        Regional.Node.Examined Reginol.Node.Positive
## Age                               -0.02396398           -0.11813829
## Stage                              0.07501922            0.34012221
## Tumor.Size                         0.09516337            0.39022509
## Regional.Node.Examined             1.00000000            0.40692674
## Reginol.Node.Positive              0.40692674            1.00000000
## Survival.Months                   -0.02528933           -0.15699916
## Sex                               -0.06026009           -0.03344945
##                        Survival.Months         Sex
## Age                         0.02531278  0.02509020
## Stage                      -0.08063557 -0.04136117
## Tumor.Size                 -0.15100312 -0.02522026
## Regional.Node.Examined     -0.02528933 -0.06026009
## Reginol.Node.Positive      -0.15699916 -0.03344945
## Survival.Months             1.00000000  0.10999706
## Sex                         0.10999706  1.00000000
#Inference
# The correlation matrix shows that all variables are moderately to strongly correlated with each other, indicating that there is some redundancy in the data.

plot(corrm.emp)

Cancer_pca <- prcomp(Cancer[-1], scale=TRUE)
summary(Cancer_pca)
## Importance of components:
##                           PC1    PC2    PC3    PC4    PC5     PC6     PC7
## Standard deviation     1.4983 1.0852 1.0303 0.9698 0.9387 0.71218 0.43271
## Proportion of Variance 0.3207 0.1682 0.1516 0.1344 0.1259 0.07246 0.02675
## Cumulative Proportion  0.3207 0.4889 0.6406 0.7749 0.9008 0.97325 1.00000
# Inference
# From the summary statistics, we can see that the first principal component (PC1) explains 32.07% of the total variance, the second principal component (PC2) explains 16.82%, and so on. The first two principal components (PC1 and PC2) together explain 48.89% of the total variance. The cumulative proportion reaches 97.33% after the sixth principal component (PC6), meaning that the remaining principal components explain very little additional variance in the data.

plot(Cancer_pca)

# A table containing eigenvalues and %'s accounted, follows. Eigenvalues are the sdev^2
(eigen_Cancer <- round(Cancer_pca$sdev^2,3))
## [1] 2.245 1.178 1.061 0.941 0.881 0.507 0.187
round(fit.pc$values, 3)
## [1] 2.245 1.178 1.061 0.941 0.881 0.507 0.187
names(eigen_Cancer) <- paste("PC",1:6,sep="")
eigen_Cancer
##   PC1   PC2   PC3   PC4   PC5   PC6  <NA> 
## 2.245 1.178 1.061 0.941 0.881 0.507 0.187
sumlambdas <- sum(eigen_Cancer)
sumlambdas
## [1] 7
## Inference
# sumlambdas is equal to 7, this suggests that the PCA extracted 7 principal components from the data, and that the sum of their corresponding eigenvalues explains all of the variation in the data.
propvar <- round(eigen_Cancer/sumlambdas,2)
propvar
##  PC1  PC2  PC3  PC4  PC5  PC6 <NA> 
## 0.32 0.17 0.15 0.13 0.13 0.07 0.03
cumvar_Cancer <- cumsum(propvar)
cumvar_Cancer
##  PC1  PC2  PC3  PC4  PC5  PC6 <NA> 
## 0.32 0.49 0.64 0.77 0.90 0.97 1.00
matlambdas <- rbind(eigen_Cancer,propvar,cumvar_Cancer)
matlambdas
##                 PC1   PC2   PC3   PC4   PC5   PC6  <NA>
## eigen_Cancer  2.245 1.178 1.061 0.941 0.881 0.507 0.187
## propvar       0.320 0.170 0.150 0.130 0.130 0.070 0.030
## cumvar_Cancer 0.320 0.490 0.640 0.770 0.900 0.970 1.000
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
rownames(matlambdas)
## [1] "Eigenvalues"         "Prop. variance"      "Cum. prop. variance"
eigvec.emp <- Cancer_pca$rotation
print(Cancer_pca)
## Standard deviations (1, .., p=7):
## [1] 1.4982562 1.0851943 1.0302880 0.9698062 0.9386874 0.7121769 0.4327057
## 
## Rotation (n x k) = (7 x 7):
##                                PC1        PC2          PC3         PC4
## Age                    -0.21487519  0.2043145  0.027261393  0.85973142
## Stage                   0.56017028 -0.3373169  0.011318788  0.11956737
## Tumor.Size              0.57902017 -0.2934857 -0.007289973  0.15966422
## Regional.Node.Examined  0.23910247  0.6987477  0.329462796 -0.11137816
## Reginol.Node.Positive   0.45785153  0.3946611  0.191113542  0.03278061
## Survival.Months        -0.18008353 -0.1898301  0.618720758 -0.33346116
## Sex                    -0.07446786 -0.2798176  0.686432853  0.31047844
##                                PC5         PC6         PC7
## Age                    -0.41336263 -0.03629602 -0.00410619
## Stage                  -0.21766761  0.18269976 -0.69082826
## Tumor.Size             -0.13361696  0.13694401  0.71864375
## Regional.Node.Examined -0.03947383  0.57624593  0.00365182
## Reginol.Node.Positive   0.10540722 -0.76394463 -0.04789123
## Survival.Months        -0.63971799 -0.15748760  0.05900235
## Sex                     0.58479969  0.07795267 -0.02241484
# Taking the first four PCs to generate linear combinations for all the variables with four factors
pcafactors.emp <- eigvec.emp[,1:6]
pcafactors.emp
##                                PC1        PC2          PC3         PC4
## Age                    -0.21487519  0.2043145  0.027261393  0.85973142
## Stage                   0.56017028 -0.3373169  0.011318788  0.11956737
## Tumor.Size              0.57902017 -0.2934857 -0.007289973  0.15966422
## Regional.Node.Examined  0.23910247  0.6987477  0.329462796 -0.11137816
## Reginol.Node.Positive   0.45785153  0.3946611  0.191113542  0.03278061
## Survival.Months        -0.18008353 -0.1898301  0.618720758 -0.33346116
## Sex                    -0.07446786 -0.2798176  0.686432853  0.31047844
##                                PC5         PC6
## Age                    -0.41336263 -0.03629602
## Stage                  -0.21766761  0.18269976
## Tumor.Size             -0.13361696  0.13694401
## Regional.Node.Examined -0.03947383  0.57624593
## Reginol.Node.Positive   0.10540722 -0.76394463
## Survival.Months        -0.63971799 -0.15748760
## Sex                     0.58479969  0.07795267
# Multiplying each column of the eigenvector’s matrix by the square-root of the corresponding eigenvalue in order to get the factor loadings
unrot.fact.emp <- sweep(pcafactors.emp,MARGIN=2,Cancer_pca$sdev[1:6],`*`)
unrot.fact.emp
##                               PC1        PC2          PC3         PC4
## Age                    -0.3219381  0.2217210  0.028087086  0.83377290
## Stage                   0.8392786 -0.3660544  0.011661611  0.11595719
## Tumor.Size              0.8675206 -0.3184890 -0.007510772  0.15484336
## Regional.Node.Examined  0.3582368  0.7582769  0.339441563 -0.10801524
## Reginol.Node.Positive   0.6859789  0.4282840  0.196901988  0.03179084
## Survival.Months        -0.2698113 -0.2060025  0.637460570 -0.32339272
## Sex                    -0.1115719 -0.3036565  0.707223528  0.30110393
##                                PC5         PC6
## Age                    -0.38801831 -0.02584919
## Stage                  -0.20432186  0.13011455
## Tumor.Size             -0.12542456  0.09752836
## Regional.Node.Examined -0.03705358  0.41038905
## Reginol.Node.Positive   0.09894443 -0.54406372
## Survival.Months        -0.60049525 -0.11215904
## Sex                     0.54894413  0.05551609
# Computing communalities
communalities.emp <- rowSums(unrot.fact.emp^2)
communalities.emp
##                    Age                  Stage             Tumor.Size 
##              0.9999968              0.9106437              0.9033031 
## Regional.Node.Examined  Reginol.Node.Positive        Survival.Months 
##              0.9999975              0.9995706              0.9993482 
##                    Sex 
##              0.9999059
# Performing the varimax rotation. The default in the varimax function is norm=TRUE thus, Kaiser normalization is carried out
rot.fact.emp <- varimax(unrot.fact.emp)
#View(unrot.fact.emp)
rot.fact.emp
## $loadings
## 
## Loadings:
##                        PC1    PC2    PC3    PC4    PC5    PC6   
## Age                    -0.107                0.993              
## Stage                   0.945                             -0.105
## Tumor.Size              0.928                             -0.167
## Regional.Node.Examined         0.980                      -0.194
## Reginol.Node.Positive   0.239  0.220                      -0.941
## Survival.Months                                    -0.994       
## Sex                                   0.998                     
## 
##                  PC1   PC2   PC3   PC4   PC5   PC6
## SS loadings    1.830 1.011 1.000 0.999 1.004 0.969
## Proportion Var 0.261 0.144 0.143 0.143 0.143 0.138
## Cumulative Var 0.261 0.406 0.549 0.691 0.835 0.973
## 
## $rotmat
##              [,1]        [,2]        [,3]        [,4]       [,5]        [,6]
## [1,]  0.814726239  0.24618023 -0.07457614 -0.21390663  0.1823229 -0.43710088
## [2,] -0.439958445  0.70276665 -0.28025689  0.20217479  0.1924468 -0.39509654
## [3,]  0.005969577  0.33231165  0.68621305  0.02673842 -0.6180267 -0.18966543
## [4,]  0.195844185 -0.11019603  0.31084616  0.86017751  0.3346397 -0.03142433
## [5,] -0.245524198 -0.03787138  0.58518604 -0.41424811  0.6422905 -0.10817742
## [6,]  0.209726035  0.56701489  0.07705898 -0.03387497  0.1524624  0.77728935
# The print method of varimax omits loadings less than abs(0.1). In order to display all the loadings, it is necessary to ask explicitly the contents of the object $loadings
fact.load.emp <- rot.fact.emp$loadings[,1:6]
fact.load.emp
##                                PC1          PC2          PC3          PC4
## Age                    -0.10653554 -0.005943569  0.011264086  0.993246278
## Stage                   0.94506454  0.021975085 -0.025493504 -0.073246335
## Tumor.Size              0.92844301  0.030233975  0.001659601 -0.068313774
## Regional.Node.Examined  0.03429352  0.979885765 -0.029934222 -0.005713421
## Reginol.Node.Positive   0.23946175  0.219548327 -0.010212504 -0.050094005
## Survival.Months        -0.06480554 -0.004576002  0.054719191  0.007488852
## Sex                    -0.01724897 -0.028339093  0.997837889  0.011107489
##                                 PC5          PC6
## Age                    -0.007533772  0.043472853
## Stage                   0.002773981 -0.104838608
## Tumor.Size              0.087645663 -0.167425560
## Regional.Node.Examined  0.004082260 -0.194164824
## Reginol.Node.Positive   0.077041096 -0.940998477
## Survival.Months        -0.993817418  0.066363802
## Sex                    -0.054055839  0.008912666
# Computing the rotated factor scores for the 30 European Countries. Notice that signs are reversed for factors F2 (PC2), F3 (PC3) and F4 (PC4)
scale.emp <- scale(Cancer[-1])
scale.emp
##                Age      Stage  Tumor.Size Regional.Node.Examined
##   [1,]  1.49983377 -1.0393086 -1.16262136             1.21298312
##   [2,] -0.46330245  0.2231849  0.10298027            -0.03829778
##   [3,]  0.40920254  1.4856783  1.24610431            -0.03829778
##   [4,]  0.40920254 -1.0393086 -0.59105933            -1.53983486
##   [5,] -0.79049182  0.2231849  0.34793542            -1.41470677
##   [6,] -0.35423933 -1.0393086 -0.50940762             0.46221458
##   [7,] -0.35423933 -1.0393086 -0.99931792            -0.41368205
##   [8,] -1.55393369  0.2231849 -0.10114903            -0.66393823
##   [9,] -1.55393369  2.7481718  2.87913866             0.71247076
##  [10,]  1.60889690  2.7481718 -0.01949731             0.83759885
##  [11,]  1.49983377 -1.0393086 -0.79518863            -0.66393823
##  [12,] -0.89955495  1.4856783  1.08280088            -0.41368205
##  [13,]  1.17264440  0.2231849  0.10298027            -0.16342587
##  [14,] -0.68142870 -1.0393086 -0.71353691             1.08785503
##  [15,]  0.84545503  0.2231849  0.10298027             0.21195840
##  [16,]  0.73639191 -1.0393086 -0.55023347             0.71247076
##  [17,]  0.19107629  0.2231849  0.55206471            -1.66496295
##  [18,] -1.22674432  0.2231849 -0.34610418             0.96272694
##  [19,] -0.68142870  0.2231849 -0.30527832             0.21195840
##  [20,]  0.62732878  0.2231849 -0.14197489             0.71247076
##  [21,] -0.68142870  0.2231849 -0.10114903             0.08683031
##  [22,]  0.30013941  0.2231849  0.30710956             0.08683031
##  [23,]  0.08201317  0.2231849 -0.14197489            -1.28957868
##  [24,] -0.68142870  1.4856783  1.53188532             0.46221458
##  [25,]  0.84545503 -1.0393086 -0.50940762             1.46323930
##  [26,]  0.95451816  0.2231849 -0.42775590             2.08887975
##  [27,] -0.68142870  0.2231849  0.71536815             1.33811121
##  [28,] -0.89955495 -1.0393086 -0.63188519            -0.03829778
##  [29,]  0.30013941  0.2231849 -0.30527832            -0.03829778
##  [30,]  1.28170753  0.2231849 -0.46858176            -0.53881014
##  [31,] -0.79049182  0.2231849  0.30710956            -1.41470677
##  [32,] -0.13611308 -1.0393086 -0.71353691            -1.16445059
##  [33,]  0.51826566 -1.0393086 -0.71353691            -1.03932250
##  [34,]  0.62732878 -1.0393086 -0.50940762             0.58734267
##  [35,] -0.89955495  0.2231849 -0.10114903             0.58734267
##  [36,] -0.35423933 -1.0393086 -0.91766620            -0.66393823
##  [37,] -0.02704996  0.2231849 -0.22362660             0.83759885
##  [38,] -0.35423933 -1.0393086 -0.59105933            -0.03829778
##  [39,] -0.57236557  0.2231849  0.10298027            -0.53881014
##  [40,] -0.35423933  0.2231849 -0.38693004             0.08683031
##  [41,]  0.30013941  1.4856783  1.53188532            -0.28855396
##  [42,]  1.06358128 -1.0393086 -0.63188519            -0.28855396
##  [43,]  0.84545503  0.2231849 -0.46858176            -1.53983486
##  [44,] -0.13611308  0.2231849 -0.38693004             0.08683031
##  [45,]  0.08201317 -1.0393086 -1.12179550            -0.41368205
##  [46,]  1.28170753  1.4856783  0.75619401            -0.53881014
##  [47,] -1.33580744 -1.0393086 -0.95849206             0.08683031
##  [48,]  0.84545503 -1.0393086 -0.71353691            -0.28855396
##  [49,] -0.13611308  0.2231849 -0.01949731             0.21195840
##  [50,]  1.60889690 -1.0393086 -1.12179550            -0.78906632
##  [51,] -1.88112306  0.2231849 -0.38693004             0.33708649
##  [52,]  1.60889690  1.4856783  0.91949744            -0.66393823
##  [53,]  0.62732878  1.4856783  3.57317826            -0.91419441
##  [54,]  0.95451816  1.4856783  1.81766633             0.71247076
##  [55,]  0.30013941 -1.0393086 -1.24427307             0.21195840
##  [56,]  0.08201317 -1.0393086 -0.87684034            -0.16342587
##  [57,]  0.84545503  0.2231849 -0.30527832             0.58734267
##  [58,] -0.46330245 -1.0393086 -0.59105933             4.34118537
##  [59,] -0.46330245 -1.0393086 -0.71353691             0.08683031
##  [60,]  0.08201317 -1.0393086 -0.83601449             0.33708649
##  [61,]  0.19107629 -1.0393086 -0.59105933             1.21298312
##  [62,] -0.35423933 -1.0393086 -0.63188519            -0.28855396
##  [63,] -1.33580744  0.2231849 -0.26445246            -1.66496295
##  [64,]  0.51826566  1.4856783  1.73601462             0.71247076
##  [65,]  1.39077065 -1.0393086 -0.79518863             0.21195840
##  [66,] -0.89955495 -1.0393086 -0.71353691            -1.16445059
##  [67,] -2.53550180  1.4856783  1.53188532             1.08785503
##  [68,] -1.55393369 -1.0393086 -0.71353691             0.71247076
##  [69,]  0.40920254 -1.0393086 -0.71353691            -1.16445059
##  [70,] -0.24517620 -1.0393086 -0.63188519            -0.28855396
##  [71,] -0.57236557  1.4856783  3.98143685            -0.28855396
##  [72,]  1.06358128  0.2231849  0.06215441             1.21298312
##  [73,] -2.53550180  0.2231849 -0.10114903             0.21195840
##  [74,]  1.28170753 -1.0393086 -0.91766620             0.08683031
##  [75,]  1.39077065  0.2231849 -0.42775590             0.58734267
##  [76,]  0.19107629  1.4856783  0.91949744            -0.16342587
##  [77,]  1.28170753  0.2231849 -0.30527832            -0.41368205
##  [78,] -1.33580744  0.2231849  0.71536815            -0.91419441
##  [79,] -0.35423933  0.2231849  0.71536815            -0.66393823
##  [80,]  1.49983377 -1.0393086 -0.71353691            -0.66393823
##  [81,] -0.13611308  0.2231849 -0.10114903             0.83759885
##  [82,]  1.39077065 -1.0393086 -0.50940762            -0.53881014
##  [83,]  1.28170753  0.2231849 -0.42775590            -0.66393823
##  [84,] -0.13611308 -1.0393086 -0.71353691            -1.53983486
##  [85,] -0.35423933 -1.0393086 -0.71353691            -0.16342587
##  [86,] -0.89955495  0.2231849  0.30710956            -0.28855396
##  [87,] -0.68142870  1.4856783  3.57317826            -0.91419441
##  [88,] -0.24517620  1.4856783  1.94014391            -0.53881014
##  [89,]  0.08201317 -1.0393086 -0.63188519            -0.41368205
##  [90,]  1.17264440 -1.0393086 -1.20344721            -0.66393823
##  [91,] -0.13611308  1.4856783  1.12362674            -0.78906632
##  [92,] -2.31737555 -1.0393086 -0.75436277             0.08683031
##  [93,]  0.95451816  0.2231849 -0.26445246            -1.16445059
##  [94,] -1.00861807  0.2231849 -0.30527832             0.83759885
##  [95,]  0.51826566 -1.0393086 -0.83601449            -0.28855396
##  [96,]  0.62732878  0.2231849 -0.30527832             0.33708649
##  [97,] -0.46330245  0.2231849 -0.10114903            -1.28957868
##  [98,]  0.73639191  0.2231849 -0.30527832            -0.53881014
##  [99,] -0.46330245  2.7481718 -0.34610418            -1.41470677
## [100,]  1.49983377  0.2231849 -0.22362660            -0.03829778
## [101,] -1.77205993  1.4856783  1.53188532             2.33913593
## [102,] -0.79049182 -1.0393086 -0.67271105             1.33811121
## [103,] -1.66299681  0.2231849  0.51123885            -1.41470677
## [104,]  0.30013941  0.2231849 -0.22362660            -0.91419441
## [105,] -0.24517620  0.2231849 -0.38693004            -0.03829778
## [106,]  0.62732878  0.2231849 -0.30527832            -1.53983486
## [107,] -0.02704996  0.2231849  0.30710956            -0.41368205
## [108,]  1.49983377 -1.0393086 -0.50940762            -0.28855396
## [109,] -1.77205993  0.2231849 -0.46858176            -0.78906632
## [110,]  0.95451816  0.2231849  0.14380613             1.96375166
## [111,]  0.73639191 -1.0393086 -0.75436277             0.08683031
## [112,] -1.88112306  1.4856783  0.75619401            -1.41470677
## [113,] -0.89955495  0.2231849  0.71536815             2.46426402
## [114,] -1.00861807  0.2231849  0.51123885            -0.03829778
## [115,] -0.02704996  1.4856783  0.75619401            -1.03932250
## [116,] -0.13611308 -1.0393086 -0.55023347            -0.28855396
## [117,] -0.46330245  1.4856783  1.77684048            -0.66393823
## [118,]  1.60889690 -1.0393086 -0.50940762             0.21195840
## [119,] -0.68142870  0.2231849  0.10298027             0.08683031
## [120,] -0.13611308  0.2231849 -0.22362660             0.08683031
## [121,]  1.39077065  0.2231849  0.10298027            -0.91419441
## [122,] -1.22674432  2.7481718  0.10298027             0.08683031
## [123,] -0.46330245  0.2231849  0.71536815             0.21195840
## [124,]  0.51826566  0.2231849  0.22545784             1.08785503
## [125,] -0.13611308 -1.0393086 -0.71353691             1.08785503
## [126,]  0.84545503 -1.0393086 -0.63188519             0.21195840
## [127,] -1.66299681  0.2231849 -0.30527832            -0.16342587
## [128,]  0.51826566 -1.0393086 -0.55023347            -1.41470677
## [129,]  0.19107629 -1.0393086 -0.71353691            -0.78906632
## [130,] -1.00861807 -1.0393086 -0.59105933            -0.16342587
## [131,]  0.62732878 -1.0393086 -0.87684034            -0.03829778
## [132,] -0.46330245  0.2231849  0.51123885            -0.53881014
## [133,]  0.40920254 -1.0393086 -0.83601449            -0.78906632
## [134,] -0.46330245 -1.0393086 -0.50940762            -1.16445059
## [135,]  0.08201317  0.2231849  0.51123885            -0.78906632
## [136,] -1.88112306 -1.0393086 -0.59105933             1.71349548
## [137,] -0.89955495  0.2231849 -0.30527832            -0.28855396
## [138,]  1.17264440  0.2231849 -0.46858176             0.71247076
## [139,]  0.73639191  0.2231849  0.67454229            -0.03829778
## [140,] -0.24517620  1.4856783  1.53188532             0.46221458
## [141,] -0.02704996 -1.0393086 -1.04014378            -1.28957868
## [142,] -1.99018618 -1.0393086 -0.55023347            -0.16342587
## [143,] -0.57236557 -1.0393086 -0.63188519             1.21298312
## [144,]  0.84545503  0.2231849  0.22545784             1.08785503
## [145,] -0.02704996  0.2231849  0.06215441             0.71247076
## [146,]  0.73639191  0.2231849 -0.10114903             0.08683031
## [147,] -0.89955495 -1.0393086 -1.16262136             0.46221458
## [148,] -1.77205993  1.4856783  1.61353704            -0.16342587
## [149,]  1.28170753 -1.0393086 -0.59105933            -1.66496295
## [150,]  0.51826566  0.2231849 -0.30527832            -0.16342587
## [151,] -1.77205993 -1.0393086 -0.95849206             0.46221458
## [152,]  1.39077065  0.2231849 -0.46858176            -0.03829778
## [153,]  0.62732878 -1.0393086 -0.50940762             0.08683031
## [154,]  0.73639191 -1.0393086 -0.71353691            -0.03829778
## [155,]  1.39077065 -1.0393086 -0.59105933            -0.03829778
## [156,]  1.60889690  1.4856783  2.75666109             0.21195840
## [157,] -0.79049182 -1.0393086 -0.63188519             0.08683031
## [158,] -1.66299681 -1.0393086 -1.04014378            -1.03932250
## [159,] -0.13611308  0.2231849 -0.34610418            -1.53983486
## [160,]  0.08201317  0.2231849  0.42958714            -0.03829778
## [161,]  0.51826566  0.2231849 -0.10114903             0.46221458
## [162,] -0.13611308 -1.0393086 -1.04014378            -1.41470677
## [163,]  0.51826566 -1.0393086 -0.59105933            -1.53983486
## [164,]  0.30013941 -1.0393086 -0.83601449             0.71247076
## [165,]  0.73639191  0.2231849 -0.30527832             0.21195840
## [166,]  1.49983377  1.4856783  1.20527845            -1.41470677
## [167,] -0.02704996 -1.0393086 -0.50940762            -0.28855396
## [168,] -1.88112306  2.7481718  1.53188532             1.21298312
## [169,] -0.68142870  0.2231849  0.18463198            -0.78906632
## [170,] -0.13611308 -1.0393086 -0.79518863            -0.03829778
## [171,]  1.60889690  0.2231849  0.30710956             0.71247076
## [172,]  0.95451816  1.4856783  1.53188532            -0.41368205
## [173,] -0.57236557 -1.0393086 -0.83601449            -0.66393823
## [174,]  0.95451816 -1.0393086 -0.95849206            -0.66393823
## [175,]  0.62732878 -1.0393086 -0.91766620             1.21298312
## [176,] -1.44487056  1.4856783  0.91949744            -0.41368205
## [177,]  0.51826566 -1.0393086 -0.59105933             0.33708649
## [178,] -1.22674432 -1.0393086 -0.71353691            -0.91419441
## [179,] -0.24517620  0.2231849 -0.30527832             2.08887975
## [180,]  0.73639191  0.2231849  0.71536815            -0.41368205
## [181,]  0.62732878 -1.0393086 -0.91766620             2.21400784
## [182,]  0.73639191  0.2231849 -0.10114903             1.08785503
## [183,]  0.95451816 -1.0393086 -0.79518863            -1.41470677
## [184,] -0.68142870  0.2231849  0.30710956             0.08683031
## [185,] -0.35423933  1.4856783  2.75666109            -0.03829778
## [186,]  1.28170753  0.2231849 -0.30527832            -0.03829778
## [187,]  1.49983377  1.4856783  1.45023361            -1.41470677
## [188,]  0.40920254  0.2231849 -0.30527832            -0.03829778
## [189,]  0.84545503  0.2231849 -0.38693004             2.46426402
## [190,] -0.89955495 -1.0393086 -0.71353691            -0.03829778
## [191,]  0.40920254  0.2231849 -0.42775590            -0.28855396
## [192,]  0.62732878 -1.0393086 -1.04014378            -1.53983486
## [193,]  0.84545503 -1.0393086 -0.67271105             0.58734267
## [194,] -0.13611308  0.2231849 -0.34610418            -1.16445059
## [195,] -1.33580744  1.4856783  1.73601462             0.21195840
## [196,]  0.95451816 -1.0393086 -0.87684034            -1.16445059
## [197,]  0.08201317  0.2231849  0.10298027             0.21195840
## [198,] -0.46330245  1.4856783  1.12362674            -0.53881014
## [199,] -0.24517620  0.2231849 -0.10114903             0.96272694
## [200,] -0.79049182  0.2231849 -0.30527832            -0.41368205
## [201,]  0.08201317  0.2231849 -0.30527832            -0.03829778
## [202,]  0.62732878  0.2231849 -0.30527832             0.21195840
## [203,]  1.28170753 -1.0393086 -0.83601449            -1.66496295
## [204,] -0.46330245  0.2231849 -0.30527832             0.33708649
## [205,]  1.06358128 -1.0393086 -0.63188519            -1.53983486
## [206,]  1.39077065 -1.0393086 -0.87684034            -1.03932250
## [207,]  0.19107629  0.2231849 -0.01949731             1.21298312
## [208,]  0.62732878  0.2231849 -0.46858176             0.46221458
## [209,]  0.19107629  0.2231849 -0.30527832            -0.28855396
## [210,] -0.68142870  2.7481718 -0.55023347            -1.03932250
## [211,] -1.11768119  1.4856783  1.73601462            -0.41368205
## [212,] -1.88112306  1.4856783  0.79701987             0.33708649
## [213,] -0.24517620 -1.0393086 -0.95849206             0.46221458
## [214,]  0.95451816 -1.0393086 -0.63188519            -0.66393823
## [215,] -0.02704996  0.2231849  0.10298027            -0.53881014
## [216,]  0.95451816  1.4856783  2.14427320            -1.28957868
## [217,] -1.11768119  0.2231849  0.71536815            -0.28855396
## [218,]  1.49983377  1.4856783  0.75619401             0.33708649
## [219,]  1.06358128 -1.0393086 -0.59105933            -1.28957868
## [220,] -0.46330245  1.4856783  1.73601462             1.58836739
## [221,]  0.08201317  1.4856783  1.61353704            -0.03829778
## [222,]  1.28170753  0.2231849  0.10298027             0.71247076
## [223,] -0.89955495 -1.0393086 -0.83601449             0.46221458
## [224,] -1.22674432  0.2231849 -0.38693004            -0.66393823
## [225,] -1.22674432 -1.0393086 -0.67271105            -1.53983486
## [226,] -1.22674432 -1.0393086 -0.67271105             1.58836739
## [227,]  0.51826566  1.4856783  1.00114916             0.71247076
## [228,]  0.08201317  1.4856783  0.71536815             3.46528874
## [229,]  0.73639191 -1.0393086 -0.63188519            -0.66393823
## [230,]  1.28170753  0.2231849 -0.01949731             0.08683031
## [231,]  0.08201317  0.2231849 -0.46858176             0.58734267
## [232,]  1.17264440 -1.0393086 -0.87684034            -0.91419441
## [233,]  1.60889690  0.2231849  0.30710956             0.96272694
## [234,]  0.51826566 -1.0393086 -0.71353691            -1.53983486
## [235,]  0.95451816 -1.0393086 -0.63188519             0.08683031
## [236,]  1.49983377 -1.0393086 -0.75436277             1.46323930
## [237,] -0.68142870  1.4856783  1.12362674             1.46323930
## [238,]  0.73639191  1.4856783  0.91949744            -0.28855396
## [239,] -1.22674432  2.7481718  3.57317826             1.71349548
## [240,] -1.11768119 -1.0393086 -0.87684034            -0.78906632
## [241,] -0.79049182  0.2231849  0.26628370             1.83862357
## [242,] -0.24517620  0.2231849 -0.38693004             1.96375166
## [243,]  1.60889690  0.2231849 -0.18280074            -0.66393823
## [244,] -1.66299681  0.2231849  0.18463198             0.46221458
## [245,] -1.22674432  0.2231849  0.30710956             0.08683031
## [246,]  1.06358128 -1.0393086 -0.95849206             0.46221458
## [247,]  1.28170753 -1.0393086 -0.99931792            -0.66393823
## [248,] -1.00861807  0.2231849 -0.18280074             0.46221458
## [249,] -1.88112306 -1.0393086 -0.71353691             0.08683031
## [250,] -0.46330245 -1.0393086 -0.63188519            -0.41368205
## [251,] -1.55393369  0.2231849  0.71536815            -1.03932250
## [252,] -0.24517620  0.2231849  0.63371643            -1.16445059
## [253,] -1.44487056  0.2231849 -0.10114903            -1.53983486
## [254,] -2.42643868  1.4856783  1.45023361            -0.16342587
## [255,]  1.17264440  1.4856783  3.16491967             0.58734267
## [256,]  1.39077065  0.2231849 -0.38693004             0.71247076
## [257,]  0.30013941 -1.0393086 -0.83601449            -0.16342587
## [258,]  0.95451816 -1.0393086 -0.79518863            -0.91419441
## [259,] -1.33580744  0.2231849  0.30710956             0.71247076
## [260,]  0.30013941  0.2231849 -0.10114903            -0.28855396
## [261,] -1.33580744 -1.0393086 -0.95849206            -0.41368205
## [262,] -0.89955495  0.2231849 -0.42775590            -0.66393823
## [263,] -0.79049182  0.2231849 -0.10114903            -0.66393823
## [264,]  1.39077065 -1.0393086 -0.83601449            -1.41470677
## [265,]  1.39077065 -1.0393086 -0.91766620             2.33913593
## [266,]  1.17264440  0.2231849 -0.30527832            -1.41470677
## [267,]  1.17264440 -1.0393086 -0.67271105             2.33913593
## [268,] -2.31737555  1.4856783  1.32775603            -1.41470677
## [269,]  1.06358128  0.2231849 -0.42775590            -1.28957868
## [270,]  1.28170753 -1.0393086 -0.63188519             0.71247076
## [271,] -2.20831243  1.4856783  1.12362674            -0.16342587
## [272,]  0.08201317  0.2231849 -0.42775590             0.71247076
## [273,] -0.79049182  0.2231849  0.10298027             0.46221458
## [274,]  0.40920254 -1.0393086 -0.59105933            -0.66393823
## [275,] -1.77205993  0.2231849  0.06215441            -0.41368205
## [276,]  0.30013941 -1.0393086 -1.08096964            -1.53983486
## [277,]  1.17264440  1.4856783  2.96079038            -1.28957868
## [278,] -0.24517620  1.4856783  2.75666109             1.08785503
## [279,]  1.39077065 -1.0393086 -0.50940762            -0.03829778
## [280,]  0.30013941  1.4856783  1.00114916            -0.03829778
## [281,]  0.73639191 -1.0393086 -0.91766620             0.21195840
## [282,] -1.00861807 -1.0393086 -0.63188519            -0.28855396
## [283,] -0.46330245  0.2231849 -0.30527832             0.46221458
## [284,] -0.46330245  0.2231849 -0.46858176            -0.28855396
## [285,] -0.13611308  0.2231849  0.51123885            -0.03829778
## [286,] -0.02704996  0.2231849  0.71536815            -0.91419441
## [287,]  0.40920254  0.2231849  0.10298027            -0.16342587
## [288,]  0.19107629  0.2231849  0.22545784            -0.28855396
## [289,]  1.49983377 -1.0393086 -0.67271105             1.96375166
## [290,] -1.44487056  1.4856783  4.38969544             3.34016065
## [291,]  0.73639191  0.2231849 -0.30527832             3.08990447
## [292,]  1.17264440 -1.0393086 -0.59105933             0.33708649
## [293,]  1.60889690 -1.0393086 -0.59105933            -0.41368205
## [294,] -1.22674432  0.2231849  0.06215441             0.58734267
## [295,] -0.79049182  2.7481718  1.32775603            -0.03829778
## [296,]  1.39077065 -1.0393086 -0.79518863            -0.53881014
## [297,] -1.00861807 -1.0393086 -0.50940762            -1.66496295
## [298,]  1.17264440  0.2231849 -0.14197489            -0.41368205
## [299,] -0.13611308 -1.0393086 -0.91766620             0.83759885
## [300,]  1.39077065  1.4856783  1.20527845            -0.16342587
## [301,] -1.22674432  0.2231849  0.71536815             0.46221458
## [302,] -0.79049182  0.2231849 -0.14197489             1.08785503
## [303,] -0.68142870 -1.0393086 -0.71353691             1.96375166
## [304,]  0.84545503 -1.0393086 -0.71353691             3.96580110
## [305,]  1.49983377  0.2231849  0.38876128             1.33811121
## [306,]  0.30013941  1.4856783  3.98143685            -0.53881014
## [307,] -1.55393369  0.2231849 -0.46858176             0.96272694
## [308,]  0.19107629  1.4856783  0.75619401            -0.53881014
## [309,] -0.24517620  0.2231849 -0.10114903            -1.28957868
## [310,] -1.55393369  0.2231849  0.10298027             0.58734267
## [311,] -0.35423933  0.2231849 -0.06032317            -1.28957868
## [312,]  1.39077065 -1.0393086 -0.75436277             0.08683031
## [313,] -0.02704996 -1.0393086 -0.71353691            -0.03829778
## [314,]  0.19107629  1.4856783  1.12362674             1.58836739
## [315,] -0.68142870 -1.0393086 -0.50940762            -0.28855396
## [316,]  0.30013941  0.2231849 -0.42775590            -1.28957868
## [317,] -0.79049182  1.4856783  1.94014391            -0.03829778
## [318,] -0.02704996 -1.0393086 -0.71353691            -0.03829778
## [319,] -1.44487056  1.4856783  2.75666109             1.71349548
## [320,]  1.17264440  0.2231849 -0.10114903            -0.28855396
## [321,]  0.40920254 -1.0393086 -0.99931792             0.46221458
## [322,] -1.77205993 -1.0393086 -0.71353691             0.08683031
## [323,] -1.77205993  1.4856783  1.94014391            -0.78906632
## [324,]  0.62732878  0.2231849 -0.10114903             0.58734267
## [325,]  0.40920254  0.2231849 -0.30527832             0.21195840
## [326,]  0.95451816  0.2231849 -0.34610418             0.08683031
## [327,] -0.13611308  0.2231849  0.10298027            -0.03829778
## [328,] -1.22674432 -1.0393086 -0.83601449            -1.66496295
## [329,]  0.62732878  2.7481718  0.51123885            -0.66393823
## [330,]  0.62732878  0.2231849 -0.30527832            -0.53881014
## [331,] -0.79049182  0.2231849  0.10298027             1.21298312
## [332,] -0.68142870  0.2231849 -0.18280074             0.58734267
## [333,]  0.51826566 -1.0393086 -0.63188519            -1.03932250
## [334,]  0.19107629 -1.0393086 -0.71353691             0.58734267
## [335,] -0.13611308  0.2231849 -0.01949731            -0.16342587
## [336,] -0.68142870 -1.0393086 -0.71353691            -0.41368205
## [337,] -0.24517620  1.4856783  1.12362674            -1.28957868
## [338,]  0.73639191  1.4856783  2.34840250            -0.16342587
## [339,]  1.28170753 -1.0393086 -0.87684034             0.58734267
## [340,] -1.00861807  0.2231849  0.18463198            -0.16342587
## [341,] -0.24517620  0.2231849 -0.46858176            -0.28855396
## [342,]  1.39077065 -1.0393086 -1.24427307             0.58734267
## [343,] -1.55393369  1.4856783  1.53188532             0.33708649
## [344,] -0.46330245 -1.0393086 -0.99931792            -0.66393823
## [345,]  1.17264440  0.2231849 -0.42775590             1.08785503
## [346,]  0.08201317  0.2231849  0.30710956            -0.28855396
## [347,] -0.79049182 -1.0393086 -0.79518863            -1.16445059
## [348,] -0.57236557  0.2231849 -0.01949731             0.21195840
## [349,] -0.13611308 -1.0393086 -1.12179550             1.83862357
## [350,] -0.13611308 -1.0393086 -0.59105933             0.33708649
## [351,] -1.11768119  1.4856783  0.79701987             1.21298312
## [352,] -0.02704996  0.2231849 -0.06032317             0.21195840
## [353,] -0.35423933 -1.0393086 -0.75436277            -1.03932250
## [354,] -0.89955495 -1.0393086 -1.04014378            -0.91419441
## [355,] -0.79049182 -1.0393086 -0.83601449            -1.66496295
## [356,]  1.49983377  0.2231849 -0.46858176             0.46221458
## [357,] -0.46330245 -1.0393086 -0.50940762             1.08785503
## [358,]  1.39077065  0.2231849 -0.26445246            -1.16445059
## [359,] -0.79049182 -1.0393086 -0.67271105            -1.41470677
## [360,]  1.49983377 -1.0393086 -0.71353691             0.71247076
## [361,]  0.08201317  0.2231849 -0.30527832            -0.53881014
## [362,] -0.79049182 -1.0393086 -0.50940762             1.08785503
## [363,]  0.19107629  1.4856783  1.94014391             1.21298312
## [364,] -0.35423933  0.2231849 -0.10114903            -1.53983486
## [365,] -1.44487056 -1.0393086 -0.67271105            -0.41368205
## [366,]  1.39077065 -1.0393086 -0.50940762             0.21195840
## [367,]  0.40920254 -1.0393086 -0.63188519             0.58734267
## [368,]  1.39077065  1.4856783  2.75666109             1.33811121
## [369,]  0.95451816  0.2231849  0.34793542            -0.03829778
## [370,]  1.60889690 -1.0393086 -0.67271105            -0.28855396
## [371,]  0.51826566  0.2231849 -0.30527832             1.96375166
## [372,] -1.11768119  2.7481718  3.08326796             0.21195840
## [373,]  1.17264440 -1.0393086 -0.83601449            -1.53983486
## [374,] -0.68142870  0.2231849  0.22545784             1.21298312
## [375,] -1.66299681  0.2231849 -0.34610418             1.46323930
## [376,]  0.08201317  0.2231849  0.51123885            -0.03829778
## [377,] -0.46330245  1.4856783  2.67500937            -0.03829778
## [378,] -1.66299681  0.2231849 -0.30527832             0.21195840
## [379,] -0.57236557  0.2231849 -0.10114903             0.46221458
##        Reginol.Node.Positive Survival.Months        Sex
##   [1,]           -0.62683648     -0.51850792 -0.5329113
##   [2,]            0.16309212     -0.42922373 -0.5329113
##   [3,]            0.55805642      0.15112350 -0.5329113
##   [4,]           -0.62683648      0.55290236 -0.5329113
##   [5,]           -0.62683648     -0.96492887 -0.5329113
##   [6,]           -0.42935433      0.77611283 -0.5329113
##   [7,]           -0.62683648     -0.78636049 -0.5329113
##   [8,]           -0.62683648     -2.57204428 -0.5329113
##   [9,]            2.73036007     -0.07208697 -0.5329113
##  [10,]            1.54546717      0.91003912 -0.5329113
##  [11,]           -0.62683648     -0.33993954 -0.5329113
##  [12,]           -0.23187218      0.91003912 -0.5329113
##  [13,]           -0.23187218     -0.69707630 -0.5329113
##  [14,]            0.55805642     -1.50063401 -0.5329113
##  [15,]            1.94043147     -0.33993954 -0.5329113
##  [16,]           -0.62683648     -1.00957096 -0.5329113
##  [17,]           -0.62683648      1.49038635 -0.5329113
##  [18,]           -0.62683648     -0.42922373 -0.5329113
##  [19,]           -0.62683648      1.57967054 -0.5329113
##  [20,]           -0.62683648      0.24040769 -0.5329113
##  [21,]           -0.42935433      0.41897607 -0.5329113
##  [22,]            0.16309212     -0.96492887 -0.5329113
##  [23,]           -0.62683648      0.28504979 -0.5329113
##  [24,]           -0.62683648      1.35646006 -0.5329113
##  [25,]            3.52028867      1.17789169 -0.5329113
##  [26,]            2.53287792     -0.07208697 -0.5329113
##  [27,]            3.71777082      1.35646006 -0.5329113
##  [28,]           -0.62683648      0.46361817 -0.5329113
##  [29,]           -0.03439003     -0.33993954 -0.5329113
##  [30,]           -0.62683648      0.64218655 -0.5329113
##  [31,]           -0.62683648     -0.87564468 -0.5329113
##  [32,]           -0.62683648     -1.00957096 -0.5329113
##  [33,]           -0.62683648      0.82075493 -0.5329113
##  [34,]           -0.23187218     -0.42922373 -0.5329113
##  [35,]            1.15050287     -1.81312867 -0.5329113
##  [36,]           -0.42935433      0.24040769  1.8715337
##  [37,]            0.36057427     -1.54527610  1.8715337
##  [38,]           -0.42935433      1.40110216  1.8715337
##  [39,]           -0.42935433      0.46361817  1.8715337
##  [40,]            0.16309212      1.49038635  1.8715337
##  [41,]            1.54546717     -1.32206563  1.8715337
##  [42,]           -0.42935433     -0.47386582  1.8715337
##  [43,]           -0.62683648      0.64218655  1.8715337
##  [44,]            0.36057427      0.55290236  1.8715337
##  [45,]           -0.42935433     -0.38458164  1.8715337
##  [46,]            0.16309212      0.82075493  1.8715337
##  [47,]           -0.42935433     -1.45599191  1.8715337
##  [48,]           -0.62683648     -0.56315001  1.8715337
##  [49,]            0.95302072      0.46361817  1.8715337
##  [50,]           -0.23187218      0.46361817  1.8715337
##  [51,]           -0.23187218     -0.02744488  1.8715337
##  [52,]           -0.62683648     -0.02744488  1.8715337
##  [53,]           -0.62683648      0.64218655  1.8715337
##  [54,]           -0.42935433     -0.07208697  1.8715337
##  [55,]           -0.62683648      0.10648141  1.8715337
##  [56,]           -0.62683648      0.06183931  1.8715337
##  [57,]           -0.62683648      0.86539702 -0.5329113
##  [58,]           -0.62683648      1.53502844 -0.5329113
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## [357,]           -0.42935433     -0.56315001  1.8715337
## [358,]           -0.42935433     -0.78636049  1.8715337
## [359,]           -0.62683648      0.19576560  1.8715337
## [360,]           -0.62683648      0.46361817  1.8715337
## [361,]           -0.42935433     -0.83100258  1.8715337
## [362,]           -0.62683648      1.35646006  1.8715337
## [363,]           -0.23187218     -1.09885515  1.8715337
## [364,]           -0.42935433      1.26717587  1.8715337
## [365,]           -0.42935433      1.57967054  1.8715337
## [366,]           -0.03439003      0.06183931  1.8715337
## [367,]            0.55805642      0.86539702  1.8715337
## [368,]            0.75553857      0.91003912  1.8715337
## [369,]           -0.03439003      1.57967054  1.8715337
## [370,]            0.36057427      0.59754445  1.8715337
## [371,]            1.34798502      0.77611283  1.8715337
## [372,]            1.94043147     -0.02744488  1.8715337
## [373,]           -0.62683648      1.35646006  1.8715337
## [374,]           -0.03439003     -1.00957096  1.8715337
## [375,]            1.74294932     -0.56315001  1.8715337
## [376,]            1.74294932      0.82075493  1.8715337
## [377,]            1.54546717     -0.65243420  1.8715337
## [378,]           -0.23187218      0.59754445  1.8715337
## [379,]           -0.62683648      0.64218655  1.8715337
## attr(,"scaled:center")
##                    Age                  Stage             Tumor.Size 
##             54.2480211              1.8232190             32.4775726 
## Regional.Node.Examined  Reginol.Node.Positive        Survival.Months 
##             14.3060686              4.1741425             71.6147757 
##                    Sex 
##              0.2216359 
## attr(,"scaled:scale")
##                    Age                  Stage             Tumor.Size 
##              9.1690020              0.7920833             24.4942796 
## Regional.Node.Examined  Reginol.Node.Positive        Survival.Months 
##              7.9918106              5.0637488             22.4003825 
##                    Sex 
##              0.4158964
#Logistic Regression

library(readr)
library(ggplot2)
library(cowplot)
#library(regclass)
#library(caret)
library(e1071)
library(pROC)
## Type 'citation("pROC")' for a citation.
## 
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
## 
##     cov, smooth, var
data<- read_csv("~/Downloads/BC.csv")
## Rows: 379 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (8): Survivor, Age, Stage, Tumor.Size, Regional.Node.Examined, Reginol.N...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
head(data)
## # A tibble: 6 × 8
##   Survivor   Age Stage Tumor.Size Regional.Node.Examined Reginol…¹ Survi…²   Sex
##      <dbl> <dbl> <dbl>      <dbl>                  <dbl>     <dbl>   <dbl> <dbl>
## 1        1    68     1          4                     24         1      60     0
## 2        1    50     2         35                     14         5      62     0
## 3        1    58     3         63                     14         7      75     0
## 4        1    58     1         18                      2         1      84     0
## 5        1    47     2         41                      3         1      50     0
## 6        1    51     1         20                     18         2      89     0
## # … with abbreviated variable names ¹​Reginol.Node.Positive, ²​Survival.Months
str(data)
## spc_tbl_ [379 × 8] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ Survivor              : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
##  $ Age                   : num [1:379] 68 50 58 58 47 51 51 40 40 69 ...
##  $ Stage                 : num [1:379] 1 2 3 1 2 1 1 2 4 4 ...
##  $ Tumor.Size            : num [1:379] 4 35 63 18 41 20 8 30 103 32 ...
##  $ Regional.Node.Examined: num [1:379] 24 14 14 2 3 18 11 9 20 21 ...
##  $ Reginol.Node.Positive : num [1:379] 1 5 7 1 1 2 1 1 18 12 ...
##  $ Survival.Months       : num [1:379] 60 62 75 84 50 89 54 14 70 92 ...
##  $ Sex                   : num [1:379] 0 0 0 0 0 0 0 0 0 0 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   Survivor = col_double(),
##   ..   Age = col_double(),
##   ..   Stage = col_double(),
##   ..   Tumor.Size = col_double(),
##   ..   Regional.Node.Examined = col_double(),
##   ..   Reginol.Node.Positive = col_double(),
##   ..   Survival.Months = col_double(),
##   ..   Sex = col_double()
##   .. )
##  - attr(*, "problems")=<externalptr>
## Exploratory Analysis

xtabs(~ Survivor + Age, data=data)
##         Age
## Survivor 31 32 33 34 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
##        0  1  0  0  1  0  3  2  0  1  1  1  1  2  2  0  1  1  0  5  1  1  1  3
##        1  1  1  2  0  1  3  5  6  6  4  5 10  3  5 12 15 15  6 13 11 12 18  8
##         Age
## Survivor 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
##        0  3  2  3  0  1  1  3  3  3  2  1  2  3  1  3
##        1 13  9  9 11 12 14 11  7 11  4 12 11 15 12  7
xtabs(~ Survivor + Stage, data=data)
##         Stage
## Survivor   1   2   3   4
##        0  12  28  16   3
##        1 136 132  45   7
xtabs(~ Survivor + Tumor.Size, data=data)
##         Tumor.Size
## Survivor  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
##        0  0  0  0  0  0  0  0  1  0  0  2  3  0  0  1  1  3  0  1  1  1  1  1
##        1  2  1  2  3  1  5  4  5  7  7 10  4  5 26  8 16 12  5 14 10  8  7  5
##         Tumor.Size
## Survivor 25 26 27 28 29 30 31 32 34 35 36 37 38 39 40 41 42 43 45 46 48 49 50
##        0  3  2  1  2  0  4  0  0  2  1  0  0  1  1  2  0  0  1  1  0  0  1  3
##        1 25  1  3  1  4 14  2  6  2 14  1  3  3  0  8  2  1  0  6  1  1  0  8
##         Tumor.Size
## Survivor 51 52 55 57 59 60 62 63 65 68 70 72 75 76 77 80 85 90 98 100 103 105
##        0  1  1  0  0  0  3  0  0  0  0  3  2  1  0  0  1  1  0  0   1   0   0
##        1  4  1  4  2  1  3  2  1  2  2  5  0  3  1  1  3  0  1  1   4   1   1
##         Tumor.Size
## Survivor 108 110 120 130 140
##        0   1   0   1   1   1
##        1   0   1   2   1   0
xtabs(~ Survivor + Regional.Node.Examined, data=data)
##         Regional.Node.Examined
## Survivor  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
##        0  1  1  4  3  2  0  2  2  2  1  3  3  2  3  2  3  3  2  1  4  1  0  4
##        1  6 13 10  8  8  8  8  7 19 13 15 22 15 29 21 18  7 16 14 13  4  4  7
##         Regional.Node.Examined
## Survivor 24 25 26 27 28 29 30 31 32 33 34 39 41 42 46 49
##        0  2  0  0  2  2  1  0  0  0  1  1  0  1  0  0  0
##        1  9  4  4  1  1  1  5  2  1  2  1  1  0  1  1  1
xtabs(~ Survivor + Reginol.Node.Positive, data=data)
##         Reginol.Node.Positive
## Survivor   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17
##        0  15   7   7   2   2   2   2   1   2   4   0   3   1   2   1   1   2
##        1 135  64  31  19  13  10   6   2   9   3   4   3   5   4   1   2   3
##         Reginol.Node.Positive
## Survivor  18  20  21  22  23  24  26  27  28
##        0   0   1   0   0   1   1   1   1   0
##        1   1   0   1   1   2   0   0   0   1
xtabs(~ Survivor + Survival.Months, data=data)
##         Survival.Months
## Survivor 7 8 11 12 13 14 15 16 23 24 25 31 34 37 38 39 40 41 42 44 45 47 48 49
##        0 0 0  0  1  1  2  1  4  3  2  2  1  1  1  0  1  3  1  2  1  2  2  0  1
##        1 1 1  1  0  0  0  0  0  0  0  0  1  0  1  1  0  0  1  1  0  0  0  2  7
##         Survival.Months
## Survivor 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
##        0  2  1  2  2  3  1  0  0  0  0  1  0  1  1  2  0  0  2  0  0  0  1  0
##        1  9  3  3  9  3  6  6  8  4  5  6  6  5  5  4  5  3  2  6  3  4  6  4
##         Survival.Months
## Survivor 73 74 75 76 77 78 79 80 81 82 84 85 86 87 88 89 90 91 92 93 94 95 96
##        0  0  1  0  0  0  0  1  0  0  0  0  1  0  1  0  0  1  1  0  0  1  0  0
##        1  9  7  5  5  7  3  7  2  8  8  7  6  8  6  2  6  5  7  9  4  5  4  3
##         Survival.Months
## Survivor 97 98 99 100 101 102 103 104 105 106 107
##        0  0  0  0   1   0   0   0   0   0   0   0
##        1  2  6  2   5   4   8   5   5   4   6   8
xtabs(~ Survivor + Sex, data=data)
##         Sex
## Survivor   0   1
##        0  48  11
##        1 247  73
logistic_simple <- glm(Survivor ~ Sex, data=data, family="binomial")
summary(logistic_simple)
## 
## Call:
## glm(formula = Survivor ~ Sex, family = "binomial", data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.0164   0.5298   0.5960   0.5960   0.5960  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   1.6382     0.1577  10.385   <2e-16 ***
## Sex           0.2544     0.3598   0.707     0.48    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 327.78  on 378  degrees of freedom
## Residual deviance: 327.26  on 377  degrees of freedom
## AIC: 331.26
## 
## Number of Fisher Scoring iterations: 4
# Inference
# Here the logistic regression model includes only one predictor variable, Sex. The estimated intercept is 1.6382 and the estimated coefficient for Sex is 0.2544. The p-value for Sex is 0.48, which indicates that the effect of Sex on Survivor is not statistically significant at the 0.05 level. Therefore, we cannot conclude that there is a significant association between Sex and Survivor in this model.

female.log.odds <- log(25 / 71)
female.log.odds
## [1] -1.043804
# Now you know how these are calculated
male.log.odds.ratio <- log((112 / 89) / (25/71))
male.log.odds.ratio
## [1] 1.273667
## Lastly, let's  see what this logistic regression predicts, given
## that a patient is either female or male (and no other data about them).
predicted.data <- data.frame(probability.of.Survivor=logistic_simple$fitted.values,sex=data$Sex)
predicted.data
##     probability.of.Survivor sex
## 1                 0.8372881   0
## 2                 0.8372881   0
## 3                 0.8372881   0
## 4                 0.8372881   0
## 5                 0.8372881   0
## 6                 0.8372881   0
## 7                 0.8372881   0
## 8                 0.8372881   0
## 9                 0.8372881   0
## 10                0.8372881   0
## 11                0.8372881   0
## 12                0.8372881   0
## 13                0.8372881   0
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## 15                0.8372881   0
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## 36                0.8690476   1
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## 311               0.8372881   0
## 312               0.8372881   0
## 313               0.8372881   0
## 314               0.8372881   0
## 315               0.8372881   0
## 316               0.8372881   0
## 317               0.8372881   0
## 318               0.8372881   0
## 319               0.8372881   0
## 320               0.8372881   0
## 321               0.8372881   0
## 322               0.8372881   0
## 323               0.8372881   0
## 324               0.8372881   0
## 325               0.8372881   0
## 326               0.8372881   0
## 327               0.8372881   0
## 328               0.8372881   0
## 329               0.8372881   0
## 330               0.8372881   0
## 331               0.8372881   0
## 332               0.8372881   0
## 333               0.8372881   0
## 334               0.8372881   0
## 335               0.8372881   0
## 336               0.8372881   0
## 337               0.8372881   0
## 338               0.8372881   0
## 339               0.8690476   1
## 340               0.8690476   1
## 341               0.8690476   1
## 342               0.8690476   1
## 343               0.8690476   1
## 344               0.8690476   1
## 345               0.8690476   1
## 346               0.8690476   1
## 347               0.8690476   1
## 348               0.8690476   1
## 349               0.8690476   1
## 350               0.8690476   1
## 351               0.8690476   1
## 352               0.8690476   1
## 353               0.8690476   1
## 354               0.8690476   1
## 355               0.8690476   1
## 356               0.8690476   1
## 357               0.8690476   1
## 358               0.8690476   1
## 359               0.8690476   1
## 360               0.8690476   1
## 361               0.8690476   1
## 362               0.8690476   1
## 363               0.8690476   1
## 364               0.8690476   1
## 365               0.8690476   1
## 366               0.8690476   1
## 367               0.8690476   1
## 368               0.8690476   1
## 369               0.8690476   1
## 370               0.8690476   1
## 371               0.8690476   1
## 372               0.8690476   1
## 373               0.8690476   1
## 374               0.8690476   1
## 375               0.8690476   1
## 376               0.8690476   1
## 377               0.8690476   1
## 378               0.8690476   1
## 379               0.8690476   1
## We can plot the data...
#ggplot(data=predicted.data ,aes(x=sex, y=probability.of.Survivor))+ geom_point(aes(color=sex), size=5) + xlab("Sex") 
# + ylab("Predicted probability of getting heart disease")
xtabs(~ probability.of.Survivor + sex, data=predicted.data)
##                        sex
## probability.of.Survivor   0   1
##       0.837288135593219 295   0
##       0.869047619046891   0  84
# Inference
# The table shows that 295 females and 0 males are predicted to have a survival probability of 0.837 or lower. Additionally, 0 females and 84 males are predicted to have a survival probability of 0.869 or higher. This suggests that there may be a difference in the predicted survival rates between males and females, with females having higher predicted survival rates in this particular model.
logistic <- glm(Survivor ~ ., data=data, family="binomial")
summary(logistic)
## 
## Call:
## glm(formula = Survivor ~ ., family = "binomial", data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.9390   0.1314   0.2733   0.5022   2.0329  
## 
## Coefficients:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept)             0.871555   1.343279   0.649   0.5165    
## Age                    -0.036605   0.019919  -1.838   0.0661 .  
## Stage                  -0.682074   0.364806  -1.870   0.0615 .  
## Tumor.Size              0.003787   0.010663   0.355   0.7225    
## Regional.Node.Examined  0.010036   0.025469   0.394   0.6936    
## Reginol.Node.Positive  -0.085848   0.038773  -2.214   0.0268 *  
## Survival.Months         0.070052   0.009895   7.079 1.45e-12 ***
## Sex                    -0.302243   0.424708  -0.712   0.4767    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 327.78  on 378  degrees of freedom
## Residual deviance: 221.79  on 371  degrees of freedom
## AIC: 237.79
## 
## Number of Fisher Scoring iterations: 6
# In the output the coefficients for each predictor variable give us information about the strength and direction of the relationship between that variable and the response variable (Survivor in this case).
# This represents the log-odds of the response variable when all predictor variables are equal to zero. In this case, the intercept is not statistically significant,i.e there is no evidence of a significant difference in the log-odds of survival between men and women when all other predictor variables are equal to zero.

## Now calculate the overall "Pseudo R-squared" and its p-value
ll.null <- logistic$null.deviance/-2
ll.proposed <- logistic$deviance/-2
(ll.null - ll.proposed) / ll.null
## [1] 0.3233411
## The p-value for the R^2
1 - pchisq(2*(ll.proposed - ll.null), df=(length(logistic$coefficients)-1))
## [1] 0
predicted.data <- data.frame(probability.of.Survivor=logistic$fitted.values,Survivor=data$Survivor)
predicted.data <- predicted.data[order(predicted.data$probability.of.Survivor, decreasing=FALSE),]
predicted.data$rank <- 1:nrow(predicted.data)
## Lastly, we can plot the predicted probabilities for each sample having
## heart disease and color by whether or not they actually had heart disease
ggplot(data=predicted.data, aes(x=rank, y=probability.of.Survivor)) +
geom_point(aes(color=Survivor), alpha=1, shape=4, stroke=2) +
xlab("Index") +
ylab("Predicted probability of getting heart disease")

# From Caret
pdata <- predict(logistic,newdata=data,type="response" )
pdata
##          1          2          3          4          5          6          7 
## 0.88831102 0.86578209 0.84995647 0.98116713 0.80044456 0.99045299 0.89662410 
##          8          9         10         11         12         13         14 
## 0.29775610 0.65207562 0.79641607 0.90355440 0.97497531 0.74200843 0.68591579 
##         15         16         17         18         19         20         21 
## 0.69263174 0.82862631 0.99269135 0.92431196 0.99557181 0.94929923 0.97116811 
##         22         23         24         25         26         27         28 
## 0.68917655 0.95357109 0.98978325 0.96206032 0.73883589 0.96647630 0.98749374 
##         29         30         31         32         33         34         35 
## 0.85766343 0.96120781 0.82133127 0.84593721 0.98745279 0.91255698 0.36377388 
##         36         37         38         39         40         41         42 
## 0.96678190 0.40571882 0.99489647 0.96146814 0.98903654 0.21995911 0.86185521 
##         43         44         45         46         47         48         49 
## 0.95137939 0.94644524 0.90420655 0.90687578 0.74927862 0.86320463 0.92542695 
##         50         51         52         53         54         55         56 
## 0.95014170 0.94399233 0.76562375 0.94213580 0.80863921 0.95550629 0.95580846 
##         57         58         59         60         61         62         63 
## 0.97837667 0.99809013 0.97326054 0.97377731 0.97978836 0.86460992 0.96943018 
##         64         65         66         67         68         69         70 
## 0.90313420 0.86901847 0.99740689 0.33053904 0.99080334 0.97395718 0.98365971 
##         71         72         73         74         75         76         77 
## 0.98583904 0.03415607 0.90057924 0.99134734 0.87098641 0.97547598 0.89889464 
##         78         79         80         81         82         83         84 
## 0.99486745 0.96107154 0.78788397 0.97204167 0.88877744 0.86234455 0.85705580 
##         85         86         87         88         89         90         91 
## 0.93554573 0.86087708 0.93122855 0.94382312 0.99022226 0.98491247 0.96005133 
##         92         93         94         95         96         97         98 
## 0.94212965 0.94261145 0.33001097 0.98220004 0.64680602 0.29074803 0.89981972 
##         99        100        101        102        103        104        105 
## 0.64330189 0.66323462 0.43857327 0.97829929 0.22354436 0.77211788 0.89353515 
##        106        107        108        109        110        111        112 
## 0.80265989 0.35159805 0.90097655 0.99604987 0.83947114 0.91983868 0.95123466 
##        113        114        115        116        117        118        119 
## 0.93580554 0.94443164 0.97992725 0.86139707 0.97816524 0.97616076 0.98448979 
##        120        121        122        123        124        125        126 
## 0.83772221 0.97517684 0.89367844 0.73041230 0.96781380 0.85789056 0.27683280 
##        127        128        129        130        131        132        133 
## 0.99416747 0.82470851 0.97439665 0.97971422 0.83090771 0.92734603 0.99208666 
##        134        135        136        137        138        139        140 
## 0.98894569 0.50400021 0.92675110 0.97890075 0.88246066 0.61178303 0.97977415 
##        141        142        143        144        145        146        147 
## 0.98548690 0.99720196 0.89262213 0.57376638 0.80487429 0.99295490 0.99313570 
##        148        149        150        151        152        153        154 
## 0.68855271 0.93082790 0.95519341 0.99753385 0.83012483 0.87936705 0.98994652 
##        155        156        157        158        159        160        161 
## 0.84511740 0.93693559 0.89759205 0.99728994 0.92864988 0.07629724 0.12665245 
##        162        163        164        165        166        167        168 
## 0.87357338 0.97760853 0.98801546 0.71860531 0.57395724 0.94541053 0.95169442 
##        169        170        171        172        173        174        175 
## 0.81115829 0.99531408 0.81837187 0.85206847 0.98585670 0.98230187 0.99203893 
##        176        177        178        179        180        181        182 
## 0.93941356 0.66874355 0.98138186 0.65941869 0.83593734 0.99168361 0.93283442 
##        183        184        185        186        187        188        189 
## 0.37473143 0.75758104 0.92327733 0.96005216 0.88497908 0.91845011 0.96076840 
##        190        191        192        193        194        195        196 
## 0.98449873 0.84622757 0.98505819 0.92065410 0.97088399 0.61522419 0.80090129 
##        197        198        199        200        201        202        203 
## 0.81281253 0.97721261 0.81447931 0.99354033 0.95033916 0.83701996 0.71002461 
##        204        205        206        207        208        209        210 
## 0.20809351 0.93143118 0.81240412 0.98383227 0.99216184 0.94837387 0.95335510 
##        211        212        213        214        215        216        217 
## 0.90373232 0.10518046 0.98864696 0.86704872 0.71379773 0.08775505 0.57255879 
##        218        219        220        221        222        223        224 
## 0.92880536 0.89346002 0.04082957 0.09889219 0.58087693 0.99766081 0.95996780 
##        225        226        227        228        229        230        231 
## 0.99102951 0.99713003 0.62543221 0.87658314 0.85045402 0.97165707 0.98171394 
##        232        233        234        235        236        237        238 
## 0.81064129 0.72862850 0.94182360 0.98913693 0.95130080 0.36966993 0.98288653 
##        239        240        241        242        243        244        245 
## 0.02174077 0.98060414 0.82812217 0.99146971 0.98903342 0.94197260 0.98017293 
##        246        247        248        249        250        251        252 
## 0.99446433 0.98936914 0.66627339 0.98706495 0.99255644 0.99453106 0.82242065 
##        253        254        255        256        257        258        259 
## 0.98060207 0.91375978 0.61162607 0.97553671 0.96866405 0.87868109 0.97747698 
##        260        261        262        263        264        265        266 
## 0.87893348 0.29218348 0.99449605 0.95271142 0.90451448 0.99249934 0.98481589 
##        267        268        269        270        271        272        273 
## 0.89835466 0.87093308 0.58773585 0.63242696 0.49196823 0.83193614 0.68670888 
##        274        275        276        277        278        279        280 
## 0.94137556 0.89307703 0.94393100 0.53608227 0.05693409 0.99113401 0.95267409 
##        281        282        283        284        285        286        287 
## 0.98468797 0.94039036 0.37185784 0.98448323 0.90550256 0.24720238 0.72675201 
##        288        289        290        291        292        293        294 
## 0.98625297 0.89119878 0.63437802 0.98400716 0.90345653 0.77885814 0.98778348 
##        295        296        297        298        299        300        301 
## 0.91702802 0.91325564 0.98546265 0.93578215 0.99228596 0.54815770 0.98997157 
##        302        303        304        305        306        307        308 
## 0.80034463 0.94299570 0.91836870 0.58938856 0.28189003 0.96577155 0.67227472 
##        309        310        311        312        313        314        315 
## 0.96597529 0.88409384 0.93935622 0.77276640 0.93453634 0.91675800 0.99105195 
##        316        317        318        319        320        321        322 
## 0.95223994 0.86712206 0.96565703 0.50066308 0.72889107 0.99583510 0.94848242 
##        323        324        325        326        327        328        329 
## 0.87796387 0.96507921 0.93508119 0.97104152 0.98740873 0.97744406 0.91344598 
##        330        331        332        333        334        335        336 
## 0.95111325 0.99381680 0.26819322 0.99546956 0.96101694 0.92390739 0.98373194 
##        337        338        339        340        341        342        343 
## 0.85776421 0.82997707 0.98581296 0.84399168 0.96333508 0.89227749 0.82372278 
##        344        345        346        347        348        349        350 
## 0.98502493 0.87703204 0.81417199 0.99515846 0.99001685 0.90448172 0.97387529 
##        351        352        353        354        355        356        357 
## 0.98651039 0.80786933 0.71501849 0.99461920 0.99589689 0.70750322 0.91091899 
##        358        359        360        361        362        363        364 
## 0.62535931 0.97056232 0.96490666 0.71666186 0.99606075 0.51296788 0.98668537 
##        365        366        367        368        369        370        371 
## 0.99721659 0.91993048 0.97796833 0.92115206 0.98721952 0.95174672 0.93886043 
##        372        373        374        375        376        377        378 
## 0.63916542 0.99036699 0.71545376 0.75885710 0.93652006 0.54170579 0.97656218 
##        379 
## 0.97452829
data$Survivor
##   [1] 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
##  [38] 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1
##  [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1
## [112] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0
## [149] 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1
## [186] 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0
## [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1
## [260] 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1
## [297] 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1
## [334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0
## [371] 1 0 1 1 1 1 1 1 1
pdataF <- as.factor(ifelse(test=as.numeric(pdata>0.5) == 0, yes="Alive", no="Dead"))

#From e1071::
#confusionMatrix(pdataF, data$Survivor)
# From pROC
roc(data$Survivor,logistic$fitted.values,plot=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
## 
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values,     plot = TRUE)
## 
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
par(pty = "s")
roc(data$Survivor,logistic$fitted.values,plot=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values,     plot = TRUE)
## 
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
## NOTE: By default, roc() uses specificity on the x-axis and the values range
## from 1 to 0. This makes the graph look like what we would expect, but the
## x-axis itself might induce a headache. To use 1-specificity (i.e. the
## False Positive Rate) on the x-axis, set "legacy.axes" to TRUE.
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE)
## 
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage")
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage")
## 
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
## 
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
## 
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
## 
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
## If we want to find out the optimal threshold we can store the
## data used to make the ROC graph in a variable...
roc.info <- roc(data$Survivor, logistic$fitted.values, legacy.axes=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
str(roc.info)
## List of 15
##  $ percent           : logi FALSE
##  $ sensitivities     : num [1:380] 1 1 1 1 1 ...
##  $ specificities     : num [1:380] 0 0.0169 0.0339 0.0508 0.0678 ...
##  $ thresholds        : num [1:380] -Inf 0.0279 0.0375 0.0489 0.0666 ...
##  $ direction         : chr "<"
##  $ cases             : Named num [1:320] 0.888 0.866 0.85 0.981 0.8 ...
##   ..- attr(*, "names")= chr [1:320] "1" "2" "3" "4" ...
##  $ controls          : Named num [1:59] 0.298 0.904 0.22 0.749 0.869 ...
##   ..- attr(*, "names")= chr [1:59] "8" "11" "41" "47" ...
##  $ fun.sesp          :function (thresholds, controls, cases, direction)  
##  $ auc               : 'auc' num 0.86
##   ..- attr(*, "partial.auc")= logi FALSE
##   ..- attr(*, "percent")= logi FALSE
##   ..- attr(*, "roc")=List of 15
##   .. ..$ percent           : logi FALSE
##   .. ..$ sensitivities     : num [1:380] 1 1 1 1 1 ...
##   .. ..$ specificities     : num [1:380] 0 0.0169 0.0339 0.0508 0.0678 ...
##   .. ..$ thresholds        : num [1:380] -Inf 0.0279 0.0375 0.0489 0.0666 ...
##   .. ..$ direction         : chr "<"
##   .. ..$ cases             : Named num [1:320] 0.888 0.866 0.85 0.981 0.8 ...
##   .. .. ..- attr(*, "names")= chr [1:320] "1" "2" "3" "4" ...
##   .. ..$ controls          : Named num [1:59] 0.298 0.904 0.22 0.749 0.869 ...
##   .. .. ..- attr(*, "names")= chr [1:59] "8" "11" "41" "47" ...
##   .. ..$ fun.sesp          :function (thresholds, controls, cases, direction)  
##   .. ..$ auc               : 'auc' num 0.86
##   .. .. ..- attr(*, "partial.auc")= logi FALSE
##   .. .. ..- attr(*, "percent")= logi FALSE
##   .. .. ..- attr(*, "roc")=List of 8
##   .. .. .. ..$ percent      : logi FALSE
##   .. .. .. ..$ sensitivities: num [1:380] 1 1 1 1 1 ...
##   .. .. .. ..$ specificities: num [1:380] 0 0.0169 0.0339 0.0508 0.0678 ...
##   .. .. .. ..$ thresholds   : num [1:380] -Inf 0.0279 0.0375 0.0489 0.0666 ...
##   .. .. .. ..$ direction    : chr "<"
##   .. .. .. ..$ cases        : Named num [1:320] 0.888 0.866 0.85 0.981 0.8 ...
##   .. .. .. .. ..- attr(*, "names")= chr [1:320] "1" "2" "3" "4" ...
##   .. .. .. ..$ controls     : Named num [1:59] 0.298 0.904 0.22 0.749 0.869 ...
##   .. .. .. .. ..- attr(*, "names")= chr [1:59] "8" "11" "41" "47" ...
##   .. .. .. ..$ fun.sesp     :function (thresholds, controls, cases, direction)  
##   .. .. .. ..- attr(*, "class")= chr "roc"
##   .. ..$ call              : language roc.default(response = data$Survivor, predictor = logistic$fitted.values,      legacy.axes = TRUE)
##   .. ..$ original.predictor: Named num [1:379] 0.888 0.866 0.85 0.981 0.8 ...
##   .. .. ..- attr(*, "names")= chr [1:379] "1" "2" "3" "4" ...
##   .. ..$ original.response : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
##   .. ..$ predictor         : Named num [1:379] 0.888 0.866 0.85 0.981 0.8 ...
##   .. .. ..- attr(*, "names")= chr [1:379] "1" "2" "3" "4" ...
##   .. ..$ response          : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
##   .. ..$ levels            : chr [1:2] "0" "1"
##   .. ..- attr(*, "class")= chr "roc"
##  $ call              : language roc.default(response = data$Survivor, predictor = logistic$fitted.values,      legacy.axes = TRUE)
##  $ original.predictor: Named num [1:379] 0.888 0.866 0.85 0.981 0.8 ...
##   ..- attr(*, "names")= chr [1:379] "1" "2" "3" "4" ...
##  $ original.response : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
##  $ predictor         : Named num [1:379] 0.888 0.866 0.85 0.981 0.8 ...
##   ..- attr(*, "names")= chr [1:379] "1" "2" "3" "4" ...
##  $ response          : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
##  $ levels            : chr [1:2] "0" "1"
##  - attr(*, "class")= chr "roc"
## tpp = true positive percentage
## fpp = false positive precentage
roc.df <- data.frame(tpp=roc.info$sensitivities*100, fpp=(1 - roc.info$specificities)*100,thresholds=roc.info$thresholds)
roc.df
##          tpp        fpp thresholds
## 1   100.0000 100.000000       -Inf
## 2   100.0000  98.305085 0.02794842
## 3   100.0000  96.610169 0.03749282
## 4   100.0000  94.915254 0.04888183
## 5   100.0000  93.220339 0.06661567
## 6   100.0000  91.525424 0.08202615
## 7   100.0000  89.830508 0.09332362
## 8   100.0000  88.135593 0.10203633
## 9   100.0000  86.440678 0.11591645
## 10   99.6875  86.440678 0.16737298
## 11   99.6875  84.745763 0.21402631
## 12   99.6875  83.050847 0.22175174
## 13   99.3750  83.050847 0.23537337
## 14   99.3750  81.355932 0.25769780
## 15   99.3750  79.661017 0.27251301
## 16   99.3750  77.966102 0.27936141
## 17   99.3750  76.271186 0.28631903
## 18   99.3750  74.576271 0.29146575
## 19   99.0625  74.576271 0.29496979
## 20   99.0625  72.881356 0.31388354
## 21   99.0625  71.186441 0.33027501
## 22   99.0625  69.491525 0.34106855
## 23   99.0625  67.796610 0.35768597
## 24   98.7500  67.796610 0.36672190
## 25   98.4375  67.796610 0.37076389
## 26   98.4375  66.101695 0.37329464
## 27   98.4375  64.406780 0.39022512
## 28   98.1250  64.406780 0.42214605
## 29   98.1250  62.711864 0.46527075
## 30   98.1250  61.016949 0.49631565
## 31   97.8125  61.016949 0.50233165
## 32   97.8125  59.322034 0.50848405
## 33   97.8125  57.627119 0.52452507
## 34   97.5000  57.627119 0.53889403
## 35   97.1875  57.627119 0.54493174
## 36   96.8750  57.627119 0.56035824
## 37   96.8750  55.932203 0.57316259
## 38   96.8750  54.237288 0.57386181
## 39   96.5625  54.237288 0.57741708
## 40   96.5625  52.542373 0.58430639
## 41   96.5625  50.847458 0.58856221
## 42   96.2500  50.847458 0.60050732
## 43   95.9375  50.847458 0.61170455
## 44   95.9375  49.152542 0.61350361
## 45   95.6250  49.152542 0.62029175
## 46   95.6250  47.457627 0.62539576
## 47   95.3125  47.457627 0.62892959
## 48   95.0000  47.457627 0.63340249
## 49   95.0000  45.762712 0.63677172
## 50   95.0000  44.067797 0.64123365
## 51   95.0000  42.372881 0.64505395
## 52   94.6875  42.372881 0.64944082
## 53   94.3750  42.372881 0.65574715
## 54   94.0625  42.372881 0.66132665
## 55   93.7500  42.372881 0.66475400
## 56   93.7500  40.677966 0.66750847
## 57   93.7500  38.983051 0.67050913
## 58   93.4375  38.983051 0.67909525
## 59   93.1250  38.983051 0.68631233
## 60   92.8125  38.983051 0.68763079
## 61   92.8125  37.288136 0.68886463
## 62   92.5000  37.288136 0.69090415
## 63   92.1875  37.288136 0.70006748
## 64   91.8750  37.288136 0.70876391
## 65   91.8750  35.593220 0.71191117
## 66   91.5625  35.593220 0.71440811
## 67   91.2500  35.593220 0.71523613
## 68   90.9375  35.593220 0.71605781
## 69   90.6250  35.593220 0.71763359
## 70   90.3125  35.593220 0.72267866
## 71   90.0000  35.593220 0.72769025
## 72   89.6875  35.593220 0.72875978
## 73   89.3750  35.593220 0.72965169
## 74   89.0625  35.593220 0.73462410
## 75   88.7500  35.593220 0.74042216
## 76   88.4375  35.593220 0.74564353
## 77   88.4375  33.898305 0.75342983
## 78   88.1250  33.898305 0.75821907
## 79   87.8125  33.898305 0.76224042
## 80   87.5000  33.898305 0.76887082
## 81   87.5000  32.203390 0.77244214
## 82   87.1875  32.203390 0.77581227
## 83   87.1875  30.508475 0.78337105
## 84   86.8750  30.508475 0.79215002
## 85   86.5625  30.508475 0.79838035
## 86   86.2500  30.508475 0.80039459
## 87   85.9375  30.508475 0.80067293
## 88   85.6250  30.508475 0.80178059
## 89   85.3125  30.508475 0.80376709
## 90   85.3125  28.813559 0.80637181
## 91   85.0000  28.813559 0.80825427
## 92   84.6875  28.813559 0.80964025
## 93   84.3750  28.813559 0.81089979
## 94   84.0625  28.813559 0.81178120
## 95   83.7500  28.813559 0.81260832
## 96   83.4375  28.813559 0.81349226
## 97   83.1250  28.813559 0.81432565
## 98   82.8125  28.813559 0.81642559
## 99   82.8125  27.118644 0.81985157
## 100  82.5000  27.118644 0.82187596
## 101  82.1875  27.118644 0.82307171
## 102  81.8750  27.118644 0.82421564
## 103  81.5625  27.118644 0.82641534
## 104  81.5625  25.423729 0.82837424
## 105  81.2500  25.423729 0.82930169
## 106  80.9375  25.423729 0.83005095
## 107  80.6250  25.423729 0.83051627
## 108  80.3125  25.423729 0.83142192
## 109  80.0000  25.423729 0.83393674
## 110  80.0000  23.728814 0.83647865
## 111  79.6875  23.728814 0.83737108
## 112  79.3750  23.728814 0.83859668
## 113  79.0625  23.728814 0.84173141
## 114  78.7500  23.728814 0.84455454
## 115  78.4375  23.728814 0.84552731
## 116  78.1250  23.728814 0.84608239
## 117  77.8125  23.728814 0.84809202
## 118  77.5000  23.728814 0.85020525
## 119  77.1875  23.728814 0.85126125
## 120  76.8750  23.728814 0.85456213
## 121  76.5625  23.728814 0.85735961
## 122  76.2500  23.728814 0.85771382
## 123  75.9375  23.728814 0.85782739
## 124  75.6250  23.728814 0.85938382
## 125  75.3125  23.728814 0.86113708
## 126  75.0000  23.728814 0.86162614
## 127  74.6875  23.728814 0.86209988
## 128  74.3750  23.728814 0.86277459
## 129  74.0625  23.728814 0.86390728
## 130  73.7500  23.728814 0.86519600
## 131  73.4375  23.728814 0.86641540
## 132  73.1250  23.728814 0.86708539
## 133  72.8125  23.728814 0.86807027
## 134  72.8125  22.033898 0.86997578
## 135  72.5000  22.033898 0.87095974
## 136  72.1875  22.033898 0.87227989
## 137  71.8750  22.033898 0.87507826
## 138  71.5625  22.033898 0.87680759
## 139  71.2500  22.033898 0.87749796
## 140  70.9375  22.033898 0.87832248
## 141  70.6250  22.033898 0.87880729
## 142  70.3125  22.033898 0.87915027
## 143  70.3125  20.338983 0.88091386
## 144  70.3125  18.644068 0.88327725
## 145  70.0000  18.644068 0.88453646
## 146  69.6875  18.644068 0.88664505
## 147  69.3750  18.644068 0.88854423
## 148  69.0625  18.644068 0.88998811
## 149  68.7500  18.644068 0.89173813
## 150  68.4375  18.644068 0.89244981
## 151  68.1250  18.644068 0.89284958
## 152  67.8125  18.644068 0.89326852
## 153  67.5000  18.644068 0.89349759
## 154  67.1875  18.644068 0.89360680
## 155  66.8750  18.644068 0.89515127
## 156  66.5625  18.644068 0.89710808
## 157  66.2500  18.644068 0.89797335
## 158  65.9375  18.644068 0.89862465
## 159  65.6250  18.644068 0.89935718
## 160  65.3125  18.644068 0.90019948
## 161  65.0000  18.644068 0.90077789
## 162  64.6875  18.644068 0.90205537
## 163  64.3750  18.644068 0.90329536
## 164  64.0625  18.644068 0.90350546
## 165  64.0625  16.949153 0.90364336
## 166  63.7500  16.949153 0.90396943
## 167  63.4375  16.949153 0.90434414
## 168  63.1250  16.949153 0.90449810
## 169  63.1250  15.254237 0.90500852
## 170  62.8125  15.254237 0.90618917
## 171  62.5000  15.254237 0.90889738
## 172  62.1875  15.254237 0.91173798
## 173  61.8750  15.254237 0.91290631
## 174  61.5625  15.254237 0.91335081
## 175  61.2500  15.254237 0.91360288
## 176  60.9375  15.254237 0.91525889
## 177  60.9375  13.559322 0.91689301
## 178  60.6250  13.559322 0.91769836
## 179  60.3125  13.559322 0.91840941
## 180  60.0000  13.559322 0.91914440
## 181  59.6875  13.559322 0.91988458
## 182  59.3750  13.559322 0.92029229
## 183  59.0625  13.559322 0.92090308
## 184  58.7500  13.559322 0.92221470
## 185  58.4375  13.559322 0.92359236
## 186  58.1250  13.559322 0.92410967
## 187  57.8125  13.559322 0.92486945
## 188  57.5000  13.559322 0.92608903
## 189  57.5000  11.864407 0.92704857
## 190  57.1875  11.864407 0.92799795
## 191  56.8750  11.864407 0.92872762
## 192  56.5625  11.864407 0.92981663
## 193  56.2500  11.864407 0.93102822
## 194  55.9375  11.864407 0.93132986
## 195  55.6250  11.864407 0.93213280
## 196  55.6250  10.169492 0.93368538
## 197  55.3125  10.169492 0.93480876
## 198  55.0000  10.169492 0.93531346
## 199  54.6875  10.169492 0.93566394
## 200  54.3750  10.169492 0.93579385
## 201  54.0625  10.169492 0.93616280
## 202  53.7500  10.169492 0.93672782
## 203  53.4375  10.169492 0.93789801
## 204  53.1250  10.169492 0.93910832
## 205  52.8125  10.169492 0.93938489
## 206  52.5000  10.169492 0.93990196
## 207  52.1875  10.169492 0.94088296
## 208  51.8750  10.169492 0.94159958
## 209  51.5625  10.169492 0.94189810
## 210  51.2500  10.169492 0.94205113
## 211  50.9375  10.169492 0.94213272
## 212  50.6250  10.169492 0.94237362
## 213  50.6250   8.474576 0.94280358
## 214  50.3125   8.474576 0.94340941
## 215  50.0000   8.474576 0.94387706
## 216  49.6875   8.474576 0.94396166
## 217  49.3750   8.474576 0.94421199
## 218  49.0625   8.474576 0.94492109
## 219  48.7500   8.474576 0.94592788
## 220  48.4375   8.474576 0.94740955
## 221  48.1250   8.474576 0.94842814
## 222  47.8125   8.474576 0.94889083
## 223  47.5000   8.474576 0.94972047
## 224  47.1875   8.474576 0.95024043
## 225  46.8750   8.474576 0.95072621
## 226  46.5625   8.474576 0.95117396
## 227  46.5625   6.779661 0.95126773
## 228  46.2500   6.779661 0.95134010
## 229  45.9375   6.779661 0.95153690
## 230  45.6250   6.779661 0.95172057
## 231  45.6250   5.084746 0.95199333
## 232  45.3125   5.084746 0.95245701
## 233  45.0000   5.084746 0.95269275
## 234  44.6875   5.084746 0.95303326
## 235  44.3750   5.084746 0.95346310
## 236  44.0625   5.084746 0.95438225
## 237  43.7500   5.084746 0.95534985
## 238  43.4375   5.084746 0.95565737
## 239  43.1250   5.084746 0.95788813
## 240  42.8125   5.084746 0.96000957
## 241  42.8125   3.389831 0.96005175
## 242  42.5000   3.389831 0.96041028
## 243  42.5000   1.694915 0.96089267
## 244  42.1875   1.694915 0.96104424
## 245  41.8750   1.694915 0.96113968
## 246  41.5625   1.694915 0.96133798
## 247  41.2500   1.694915 0.96176423
## 248  40.9375   1.694915 0.96269770
## 249  40.6250   1.694915 0.96412087
## 250  40.3125   1.694915 0.96499294
## 251  40.0000   1.694915 0.96536812
## 252  39.6875   1.694915 0.96571429
## 253  39.3750   1.694915 0.96587342
## 254  39.0625   1.694915 0.96622579
## 255  38.7500   1.694915 0.96662910
## 256  38.4375   1.694915 0.96729785
## 257  38.1250   1.694915 0.96823893
## 258  37.8125   1.694915 0.96904711
## 259  37.5000   1.694915 0.96999625
## 260  37.1875   1.694915 0.97072316
## 261  36.8750   1.694915 0.97096276
## 262  36.5625   1.694915 0.97110481
## 263  36.2500   1.694915 0.97141259
## 264  35.9375   1.694915 0.97184937
## 265  35.6250   1.694915 0.97265111
## 266  35.3125   1.694915 0.97351892
## 267  35.0000   1.694915 0.97382630
## 268  34.6875   1.694915 0.97391623
## 269  34.3750   1.694915 0.97417692
## 270  34.0625   1.694915 0.97446247
## 271  33.7500   1.694915 0.97475180
## 272  33.4375   1.694915 0.97507608
## 273  33.1250   1.694915 0.97532641
## 274  32.8125   1.694915 0.97550634
## 275  32.5000   1.694915 0.97584873
## 276  32.1875   1.694915 0.97636147
## 277  31.8750   1.694915 0.97688740
## 278  31.5625   1.694915 0.97732834
## 279  31.2500   1.694915 0.97746052
## 280  30.9375   1.694915 0.97754275
## 281  30.6250   1.694915 0.97778843
## 282  30.3125   1.694915 0.97806679
## 283  30.0000   1.694915 0.97823226
## 284  29.6875   1.694915 0.97833798
## 285  29.3750   1.694915 0.97863871
## 286  29.0625   1.694915 0.97930748
## 287  28.7500   1.694915 0.97974418
## 288  28.4375   1.694915 0.97978125
## 289  28.1250   1.694915 0.97985780
## 290  27.8125   1.694915 0.98005009
## 291  27.5000   1.694915 0.98038750
## 292  27.1875   1.694915 0.98060311
## 293  26.8750   1.694915 0.98088564
## 294  26.5625   1.694915 0.98127450
## 295  26.2500   1.694915 0.98154790
## 296  25.9375   1.694915 0.98195699
## 297  25.6250   1.694915 0.98225095
## 298  25.3125   1.694915 0.98259420
## 299  25.0000   1.694915 0.98327312
## 300  24.6875   1.694915 0.98369583
## 301  24.3750   1.694915 0.98378211
## 302  24.0625   1.694915 0.98391972
## 303  23.7500   1.694915 0.98424520
## 304  23.4375   1.694915 0.98448651
## 305  23.1250   1.694915 0.98449426
## 306  22.8125   1.694915 0.98459335
## 307  22.5000   1.694915 0.98475193
## 308  22.1875   1.694915 0.98486418
## 309  21.8750   1.694915 0.98496870
## 310  21.5625   1.694915 0.98504156
## 311  21.2500   1.694915 0.98526042
## 312  20.9375   1.694915 0.98547478
## 313  20.6250   1.694915 0.98564993
## 314  20.3125   1.694915 0.98582600
## 315  20.0000   1.694915 0.98584787
## 316  19.6875   1.694915 0.98605484
## 317  19.3750   1.694915 0.98638168
## 318  19.0625   1.694915 0.98659788
## 319  19.0625   0.000000 0.98687516
## 320  18.7500   0.000000 0.98714224
## 321  18.4375   0.000000 0.98731413
## 322  18.1250   0.000000 0.98743076
## 323  17.8125   0.000000 0.98747326
## 324  17.5000   0.000000 0.98763861
## 325  17.1875   0.000000 0.98789947
## 326  16.8750   0.000000 0.98833121
## 327  16.5625   0.000000 0.98879632
## 328  16.2500   0.000000 0.98898955
## 329  15.9375   0.000000 0.98903498
## 330  15.6250   0.000000 0.98908674
## 331  15.3125   0.000000 0.98925304
## 332  15.0000   0.000000 0.98957620
## 333  14.6875   0.000000 0.98986489
## 334  14.3750   0.000000 0.98995905
## 335  14.0625   0.000000 0.98999421
## 336  13.7500   0.000000 0.99011956
## 337  13.4375   0.000000 0.99029463
## 338  13.1250   0.000000 0.99040999
## 339  12.8125   0.000000 0.99062816
## 340  12.5000   0.000000 0.99091642
## 341  12.1875   0.000000 0.99104073
## 342  11.8750   0.000000 0.99109298
## 343  11.5625   0.000000 0.99124068
## 344  11.2500   0.000000 0.99140853
## 345  10.9375   0.000000 0.99157666
## 346  10.6250   0.000000 0.99186127
## 347  10.3125   0.000000 0.99206280
## 348  10.0000   0.000000 0.99212425
## 349   9.6875   0.000000 0.99222390
## 350   9.3750   0.000000 0.99239265
## 351   9.0625   0.000000 0.99252789
## 352   8.7500   0.000000 0.99262390
## 353   8.4375   0.000000 0.99282313
## 354   8.1250   0.000000 0.99304530
## 355   7.8125   0.000000 0.99333801
## 356   7.5000   0.000000 0.99367856
## 357   7.1875   0.000000 0.99399213
## 358   6.8750   0.000000 0.99431590
## 359   6.5625   0.000000 0.99448019
## 360   6.2500   0.000000 0.99451356
## 361   5.9375   0.000000 0.99457513
## 362   5.6250   0.000000 0.99474332
## 363   5.3125   0.000000 0.99488196
## 364   5.0000   0.000000 0.99502747
## 365   4.6875   0.000000 0.99523627
## 366   4.3750   0.000000 0.99539182
## 367   4.0625   0.000000 0.99552069
## 368   3.7500   0.000000 0.99570345
## 369   3.4375   0.000000 0.99586599
## 370   3.1250   0.000000 0.99597338
## 371   2.8125   0.000000 0.99605531
## 372   2.5000   0.000000 0.99659539
## 373   2.1875   0.000000 0.99716599
## 374   1.8750   0.000000 0.99720927
## 375   1.5625   0.000000 0.99725327
## 376   1.2500   0.000000 0.99734842
## 377   0.9375   0.000000 0.99747037
## 378   0.6250   0.000000 0.99759733
## 379   0.3125   0.000000 0.99787547
## 380   0.0000   0.000000        Inf
head(roc.df) 
##   tpp       fpp thresholds
## 1 100 100.00000       -Inf
## 2 100  98.30508 0.02794842
## 3 100  96.61017 0.03749282
## 4 100  94.91525 0.04888183
## 5 100  93.22034 0.06661567
## 6 100  91.52542 0.08202615
## head() will show us the values for the upper right-hand corner of the ROC graph, when the threshold is so low
## (negative infinity) that every single sample is called "obese".
## Thus TPP = 100% and FPP = 100%
tail(roc.df) 
##        tpp fpp thresholds
## 375 1.5625   0  0.9972533
## 376 1.2500   0  0.9973484
## 377 0.9375   0  0.9974704
## 378 0.6250   0  0.9975973
## 379 0.3125   0  0.9978755
## 380 0.0000   0        Inf
## tail() will show us the values for the lower left-hand corner
## of the ROC graph, when the threshold is so high (infinity)
## that every single sample is called "not obese".
## Thus, TPP = 0% and FPP = 0%
## now let's look at the thresholds between TPP 60% and 80%
roc.df[roc.df$tpp > 60 & roc.df$tpp < 80,]
##         tpp      fpp thresholds
## 111 79.6875 23.72881  0.8373711
## 112 79.3750 23.72881  0.8385967
## 113 79.0625 23.72881  0.8417314
## 114 78.7500 23.72881  0.8445545
## 115 78.4375 23.72881  0.8455273
## 116 78.1250 23.72881  0.8460824
## 117 77.8125 23.72881  0.8480920
## 118 77.5000 23.72881  0.8502052
## 119 77.1875 23.72881  0.8512612
## 120 76.8750 23.72881  0.8545621
## 121 76.5625 23.72881  0.8573596
## 122 76.2500 23.72881  0.8577138
## 123 75.9375 23.72881  0.8578274
## 124 75.6250 23.72881  0.8593838
## 125 75.3125 23.72881  0.8611371
## 126 75.0000 23.72881  0.8616261
## 127 74.6875 23.72881  0.8620999
## 128 74.3750 23.72881  0.8627746
## 129 74.0625 23.72881  0.8639073
## 130 73.7500 23.72881  0.8651960
## 131 73.4375 23.72881  0.8664154
## 132 73.1250 23.72881  0.8670854
## 133 72.8125 23.72881  0.8680703
## 134 72.8125 22.03390  0.8699758
## 135 72.5000 22.03390  0.8709597
## 136 72.1875 22.03390  0.8722799
## 137 71.8750 22.03390  0.8750783
## 138 71.5625 22.03390  0.8768076
## 139 71.2500 22.03390  0.8774980
## 140 70.9375 22.03390  0.8783225
## 141 70.6250 22.03390  0.8788073
## 142 70.3125 22.03390  0.8791503
## 143 70.3125 20.33898  0.8809139
## 144 70.3125 18.64407  0.8832773
## 145 70.0000 18.64407  0.8845365
## 146 69.6875 18.64407  0.8866451
## 147 69.3750 18.64407  0.8885442
## 148 69.0625 18.64407  0.8899881
## 149 68.7500 18.64407  0.8917381
## 150 68.4375 18.64407  0.8924498
## 151 68.1250 18.64407  0.8928496
## 152 67.8125 18.64407  0.8932685
## 153 67.5000 18.64407  0.8934976
## 154 67.1875 18.64407  0.8936068
## 155 66.8750 18.64407  0.8951513
## 156 66.5625 18.64407  0.8971081
## 157 66.2500 18.64407  0.8979734
## 158 65.9375 18.64407  0.8986246
## 159 65.6250 18.64407  0.8993572
## 160 65.3125 18.64407  0.9001995
## 161 65.0000 18.64407  0.9007779
## 162 64.6875 18.64407  0.9020554
## 163 64.3750 18.64407  0.9032954
## 164 64.0625 18.64407  0.9035055
## 165 64.0625 16.94915  0.9036434
## 166 63.7500 16.94915  0.9039694
## 167 63.4375 16.94915  0.9043441
## 168 63.1250 16.94915  0.9044981
## 169 63.1250 15.25424  0.9050085
## 170 62.8125 15.25424  0.9061892
## 171 62.5000 15.25424  0.9088974
## 172 62.1875 15.25424  0.9117380
## 173 61.8750 15.25424  0.9129063
## 174 61.5625 15.25424  0.9133508
## 175 61.2500 15.25424  0.9136029
## 176 60.9375 15.25424  0.9152589
## 177 60.9375 13.55932  0.9168930
## 178 60.6250 13.55932  0.9176984
## 179 60.3125 13.55932  0.9184094
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
## 
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 85.96%
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE, print.auc=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4,     print.auc = TRUE)
## 
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 85.96%
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE, print.auc=TRUE, partial.auc=c(100, 90), auc.polygon = TRUE, auc.polygon.col = "#377eb822", print.auc.x=45)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4,     print.auc = TRUE, partial.auc = c(100, 90), auc.polygon = TRUE,     auc.polygon.col = "#377eb822", print.auc.x = 45)
## 
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Partial area under the curve (specificity 100%-90%): 4.104%
# Lets do two roc plots to understand which model is better
roc(data$Survivor, logistic_simple$fitted.values, plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, print.auc=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
## 
## Call:
## roc.default(response = data$Survivor, predictor = logistic_simple$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4,     print.auc = TRUE)
## 
## Data: logistic_simple$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 52.08%
# Lets add the other graph
plot.roc(data$Survivor, logistic$fitted.values, percent=TRUE, col="#4daf4a", lwd=4, print.auc=TRUE, add=TRUE, print.auc.y=40)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
legend("bottomright", legend=c("Simple", "Non Simple"), col=c("#377eb8", "#4daf4a"), lwd=4) 

# ggplots

library(ggplot2)
library(lattice)
library(ggridges)
library(ggvis)
library(ggthemes)
library(cowplot)
library(gapminder)
library(gganimate)
library(dplyr)
library(tidyverse)
library(grid)
library(gridExtra)
library(RColorBrewer)
library(readr)

Cancer<- read_csv("~/Downloads/BC.csv")
## Rows: 379 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (8): Survivor, Age, Stage, Tumor.Size, Regional.Node.Examined, Reginol.N...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Cancer
## # A tibble: 379 × 8
##    Survivor   Age Stage Tumor.Size Regional.Node.Examined Regino…¹ Survi…²   Sex
##       <dbl> <dbl> <dbl>      <dbl>                  <dbl>    <dbl>   <dbl> <dbl>
##  1        1    68     1          4                     24        1      60     0
##  2        1    50     2         35                     14        5      62     0
##  3        1    58     3         63                     14        7      75     0
##  4        1    58     1         18                      2        1      84     0
##  5        1    47     2         41                      3        1      50     0
##  6        1    51     1         20                     18        2      89     0
##  7        1    51     1          8                     11        1      54     0
##  8        0    40     2         30                      9        1      14     0
##  9        1    40     4        103                     20       18      70     0
## 10        1    69     4         32                     21       12      92     0
## # … with 369 more rows, and abbreviated variable names ¹​Reginol.Node.Positive,
## #   ²​Survival.Months
str(Cancer)
## spc_tbl_ [379 × 8] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ Survivor              : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
##  $ Age                   : num [1:379] 68 50 58 58 47 51 51 40 40 69 ...
##  $ Stage                 : num [1:379] 1 2 3 1 2 1 1 2 4 4 ...
##  $ Tumor.Size            : num [1:379] 4 35 63 18 41 20 8 30 103 32 ...
##  $ Regional.Node.Examined: num [1:379] 24 14 14 2 3 18 11 9 20 21 ...
##  $ Reginol.Node.Positive : num [1:379] 1 5 7 1 1 2 1 1 18 12 ...
##  $ Survival.Months       : num [1:379] 60 62 75 84 50 89 54 14 70 92 ...
##  $ Sex                   : num [1:379] 0 0 0 0 0 0 0 0 0 0 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   Survivor = col_double(),
##   ..   Age = col_double(),
##   ..   Stage = col_double(),
##   ..   Tumor.Size = col_double(),
##   ..   Regional.Node.Examined = col_double(),
##   ..   Reginol.Node.Positive = col_double(),
##   ..   Survival.Months = col_double(),
##   ..   Sex = col_double()
##   .. )
##  - attr(*, "problems")=<externalptr>
# Scatter plot
ggplot(Cancer, aes(x=Age,y=Stage))+geom_point(aes(color=Survivor)) 

## We can see from the graph that there are no deaths for any age group in stage 1 of cancer.
## In stage 2 there are negligle deaths.
## In stage 3 30-40 and 50-60 years age group there are few deaths.
## In stage 4 death rates are more.
ggplot(Cancer, aes(x=Stage,y=Tumor.Size))+geom_point(aes(color=Survivor)) 

## From this graph we can infere that death rates are more in stage 3 and 4 for tumor size 50 and above.

ggplot(Cancer, aes(x=Age,y=Survival.Months)) + facet_wrap(~Stage) + geom_point(aes(color=Survivor))

# Histogram

ggplot(Cancer, aes(Stage))+geom_histogram(fill='coral', color='white',bins=10)

ggplot(Cancer, aes(Sex))+geom_histogram(aes(fill=after_stat(count)))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

# We can see from this graph that stage 1 & 2 patients are more.

# Bar chart

ggplot(Cancer, aes(Survivor))+ geom_bar(position="stack", fill='seagreen') 

## Number of survivors are more compared to non-survivors.
ggplot(Cancer, aes(Stage)) + facet_grid(.~Survivor) + geom_bar(position="dodge",fill='violet')

# box plot

ggplot(Cancer, aes(x=Survivor,y=Age)) + geom_boxplot()
## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?

ggplot(Cancer, aes(x=Survival.Months,y=Stage)) + geom_boxplot() + coord_flip()
## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?

# hexbin

ggplot(Cancer, aes(x=Age, y=Stage)) + geom_hex()